If you have problems, disadvantage on attacks isn't one of them
The portion of the ability you're concerned about is roughly equivalent to everyone having disadvantage against your monster, always. Let's compare this to something the Dungeon Master's Guide has guidance on: Superior Invisibility.
According to the Monster Features table, a creature that can be invisible as long as its concentrating effectively increases its AC by 2. Your ability is sometimes better than invisibility, and sometimes worse.
- It's better in cases where the player characters could normally thwart invisibility with Truesight or similar.
- It's worse when the player characters rely on spells and other abilities that require a target they can see.
- It's better because it doesn't require concentration.
- It's worse because if people stay more than 30 feet away, they're safe.
In fact, that last point is crucial if you're playing with flanking rules. Characters who do their combat up close will be affected by Exhaustion Pulse, but are likely to be able to gain advantage through flanking, and will circumvent the disadvantage entirely.
I think, from this comparison, it's not unreasonable to say that Exhaustion Pulse should be close in value to Superior Invisibility. That means it will increase the effective AC of your monster by something like 2 or 3. This is not, on its own, unreasonable - the existing CR 30 monsters that we have as examples both have AC 25, which would be about on par with your monster's AC.
Normally I'd be concerned about stacking Magic Resistance on top of that, but lo and behold, both other CR 30 monsters have that (or a better version) as well.
Look at the rest of the package
There are a couple causes for concern, however. Disadvantage on saving throws is huge, depending upon what other abilities your monster (or its minions) have. If your estimate of 263 damage per round relied on saves, for example, then Exhaustion Pulse has the potential to drastically increase your damage output. Similarly, if it has access to must-save abilities such as the feeblemind spell... Well, that'll make short work of any of your player character spellcasters.
It's also somewhat concerning that the effect of Exhaustion Pulse lasts for 3 rounds. That's unusual, to say the least: typically, abilities like this will either last for a single round, or until the target succeeds on its save. It's important to note that if a target failed once, it's nearly guaranteed to do so a second time, since it has disadvantage on the save against the legendary action.
So the likely play pattern is to use your legendary actions for other things for the intervening two rounds, then on the third round do the pulse again while anyone already under its effect is likely to fail. That's going to be both frustrating and more powerful than the effect looks on its face.
Is there a better way?
I think you'd do well to look at examples of similar themes here. There's a couple ways you could intend the ability to play out, and in my opinion your wording isn't great for either of them.
This ability is a challenge to be overcome
If you want your monster to seem horrifying and unbeatable at first, but for the tides to turn in your players' favour as the battle goes on, look at the Frightful Presence ability dragons share:
A creature can repeat the saving throw at the end of each of its turns, ending the effect on itself on a success. If a creature's saving throw is successful or the effect ends for it, the creature is immune to the dragon's Frightful Presence for the next 24 hours.
Wording like this makes it less likely that this is a repetitive annoyance, and more likely that players can actually plan around it.
This ability represents inevitability
If you want a drawn out combat with your monster to be effectively futile, you've chosen the wrong condition to impose. Your Exhaustion Pulse should actually be imposing the actual exhaustion condition.
The first level of exhaustion is a minor annoyance, but anyone who understands the mechanic should be instantly terrified if they see a monster causing on-demand exhaustion. Playing the long game against this thing would be a terrible idea, and it means being in its presence isn't just problematic; it will kill you, likely within a minute or two, without ever touching your HP.
You need to be quite careful about this, though. Exhaustion is a nasty mechanic, and the best example I have of an existing monster that uses it in this way, the sibriex, has a number of safety measures to keep it from getting out of hand.
On the other hand...
This is a CR 30 monster. You players should expect it to get out of hand.