This monster is weird
Though this isn't necessarily a bad thing, monster are meant to be strange creatures, this is a fantasy game after all and throwing in a completely alien monster, that breaks with the norm once in a while can be a fun experience for your group. However I fear this one is a tad to different in many of its qualities which I am going to assess below.
It is smart and dumb at the same time
So it can understand all languages, not talk directly but speak telepathically to everyone in a 1 mile radius? That sounds like a powerful psychic being, if there wasn't one little catch: it has an INT score of literally 1. I assure you, you will have more profound conversations with a new born baby than with this thing, that is probably not even aware of its own existence. The inner machinations of this mind truly are an enigma.
Its defenses are pathetically weak and unbeatably strong
You said your goal is for this to be a fair fight for any sort of group. I assure you this is not going to be the case with its current defenses.
As pointed out by the other answer its AC of 10 will mean it will be hit by every single physical attack thrown at it and its immunity to non-magical damage will not be of any use either, as you can assume most players will have magical weapons by this point (unless you as the DM don't hand them out in your game). With that an average Level 20 Fighter will be able to deal roughly 40 damage to it per turn, double that if he action surges.
And then we look at its magical defenses and wonder how any Wizard or Sorcerer is supposed to make a dent on this thing. It is immune to every spell of 6th level or lower, which means a Level 20 Spellcaster only has 4 Spell slots to use one it. 90% of the time all of these are going to be useless aswell because, it has advantage on saving throws against spells and spell attacks against it are made with disadvantage and it also has relatively good saves in CON, DEX and WIS, which are the three most common saves. And if that wasn't enough it still has 3 legendary resistances.
All of my above statements are without taking into account the Retune ability, which deflects 60% of all damage dealt to it all the time and which I am going to discuss later.
It can easily be defeated without a fight
If your Spellcasters manage to burn through its 3 resistances they can take it out instantly with any crowd control spell that targets CHA, STR or INT, other than those that send it to another plane of existence of course, as it's immune to them. This is because it has the lowest possible save in these three stats and even the advantage is not going to save it, as your monster can never roll higher than a 15 on saves made with those stats and a Level 20 Character is easily going to have a save DC greater than that. I struggle to find an example for this right now, but there is one for sure.
Retune is frustrating for the DM and the Players
First of all as you are already aware the retune ability is hard to calculate its CR for, this I am going to discuss in the next segment, where I try to puzzle out its offensive challenge rating. I just wanted to mentioned this here as one factor, that makes this monster difficult for you as the DM.
The other problem with retune is it being used in the game:
For you as the DM: Let me get this straight, everytime this thing takes damage you want to Roll a d10 to see if it actually takes some or reflects, then if it reflects you want to randomly determine a damage type (presumably by rolling a d8) and then roll the damage in the end? This going to be a lot of work during the session, and for what exactly?
For your Players: And then think of your players. How do you think they will feel if 60% of all damage they deal to it doesn't harm it, but them instead? How will your wizard feel if he rejoices, that he finally managed to get this thing to fail a saving throw, but then you tell them it ignores that damage and deals some back to them instead?
Its damage output goes through the roof
To calculate its OCR we need to look at its damage dealing abilites, which thankfully is only one, Harmful Frequency (plus Retune, but to that later). This is a fine ability by itself and it's no problem if this is its only damaging ability. It just uses this every turn, why not and if you want to choose a damage type everytime it is used, that's up to you.
It has a save of 19 and deals an average of 14 damage per use. This gives us an OCR of 6 as we need to double the damage to 28 because of it being able to hit multiple targets.
But then we realise we need to quadruple the damage per round because this creature, for some reason, is able to use its most powerful damage dealing ability as a legendary action, costing only one action. That's like if a Wizard casts fireball on his turn, but then also 3 times when it isn't his turn. This will gives us an OCR of 18 instead of the previous 6.
As I said Harmful Frequency by itself is not a bad ability. But a Monster should not be able to burst damage if it isn't their turn. If it can deal a larger amount of damage with a legendary action it should not be as much as its most powerful ability and should use atleast 2 if not 3 legendary actions. Look at a Dragon's Wing Attack as an example here.
And then we get to Retune, and its potential damage output per round sky rockets to become effectively infinite. Retune is a passive ability that gets actived every single time it takes any damage and most of the time then deals damage back to everyone around it. Not only is this frustrating for you and the players as discussed above, this also gives the Retuned String a really unusual optimal battle strategy: Take as much damage as you can. The String is encouraged to get hit by its enemies and allies at any possible opportuniy and maybe even teleport itself 10 feet above the ground to take some fall damage.
Its healing abilities are unheard of
Healing itself. The String can heal 20 HP as a legendary action, though this will cost all three of them. This means it can heal itself up from 1 HP back to its (average) max of 255 within 13 rounds or little over 2 Minutes. It never needs to take a rest. If your players leave the room and come back it is going to be fully healed and they will have to start over.
Healing others. Its Healing Frequency can heal 3/day that seems reasonable, but 60 HP is a lot, especially if you can heal a group of unlimited size. That means it can heal up all damage your players did to all of the minions it might have fighting by its side and that three times, effectivly giving them 4 x the amount of hit points. This can end up making the fight impossible and again frustrating your players: "You couldn't deal damage to it, so you tried to deal damage to its minions? Too bad, it can heal them all up in an instant multiple times."
Lastly regarding the restored conditions I would advice to just make it so it casts lesser or greater restoration, instead of giving us a list of conditions to tick off.
It has the CR of a world ending disaster, but the stats of a rat
At first I wanted the second part of this headline to be a joke, but looking at a rat's stats this is actually really accurate.
The Retuning String has the following Ability modifiers:
-5 STR +0 DEX +4 CON -5 INT +0 WIS -5 CHA
While a rat has:
-4 STR +0 DEX -1 CON -4 INT +0 WIS -3 CHA
That means a measly CR 0 rat beats your supposed CR 24 monster in 3 of its abilities, ties it in 2 and only looses to it when you compare constitution. This really doesn't make this feel like the epic creature a high CR monster is supposed to be.
What comes to your mind when you picture a monster of CR 20+? For me its a creature that can by itself be a threat to the existence of an entire campaign world and potentially the endboss of a Level 20 Campaign, either by being a ferocious monster or a high level Spell Caster. Your Monster here is on par in its strength with the above, but is simply a medium-sized String that wiggles around to make noises. I would suggest to either lower its CR or increase its grandeur to match it.
Just to finish what I started earlier, let me calculate the CR myself. I came up with the OCR of 18 (and I am not including Retune for the sake of my sanity) now we only need the DCR. This would be a DCR 19 in my calculation, calculated with the AC 10, 255 HP + the legendary resistances, Magic Resistance and Save Proficiencies increasing it further. Giving us a final CR of either 18 or 19 (your choice) if we go by these tangible numbers, but obviously even higher because of Retune.
What changes I would suggest:
Rethink its mental ability. As stated above and also pointed out by the other answer.
Increase its AC. This was also pointed out by the other answer. I personally would fix it by increasing its Dexterity and then giving it some natural armor, let's say around 4-5 points.
Make it less immune to spells. I would just keep it at a simple advantage against spell saves, no disadvantage of attacks and no immunity to lower level spells.
Make it deal most of its damage on its turn. See my statement regarding Harmful Frequency as a Legendary Action in the section about damage.
Limit its choice of Damage Types. Different Damage Types really aren't that useful to a monster, as most player characters take normal damage from all but 1-2 types. I suggest just stick to either Force Damage, if you want to make it feel like a monster made from energy or Thunder Damage if you want to lean into its sound theme.
Make its healing less potent. Maybe just make it able to Cast Mass Healing Word 1-3 times a day?
Completely rework Retune. As Pyrotechnical stated in one of his comments, make this ability a reaction, which means it can only use it once per turn, or make it atleast not deal any damage and find a way to make it less frustrating for everyone at the table.
Adjust its stats to fit its theme. As discussed above a CR20+ creature typically has neither the stats of a tiny rodent nor the unassumingness of a piece of string. So I would suggest either adjusting its stats up, its CR down or making it look and sound as a being this powerful is meant to be.