Consider aiming at mechanically balanced homebrew content
I think in general it is problematic to propose homebrew mechanics for your character that are strictly superior than the offically available options, if you do not balance it with some downside. Asking for more can create the impression of using the pretense of a character concept to get an unfair advantage in power, compared to other players. In general it is better to aim at something that is balanced with the normally available options. If you primarily care about the character concept, you should really not need game-mechanics upsides over the baseline of power to play it.
So the key question is if what you propose is in line with the overall balance of the game for your group, not how it compares to an individual magic item. If the proposal is balanced, or the group plays at a slightly overpowered level anyways, I would not worry. If it is too good, I would revise it. In any case, be gracious and accept what the DM decides about it in the end.
Assessing your proposed mechanics
A real improvised weapon is a lot weaker than what you call an "Improvised weapon" in your original design1. It deals d4 damage, not 1d8, and has a range of 20/60, not 30/120, and you cannot use your proficiency bonus on the attack without a special feature to do so, like Tavern Brawler.
When you can add your proficiency bonus, your proposed mechanic instead is better weapon than a Javelin, which has 30/120 feet of thrown range, but only deals 1d6 plus Strength modifier in damage.
As another comparison, longbows deal 1d8 as you proposed, at even greater range, but are two-handed so no extra +2 to AC, wich seems to be a significant cost. You can shoot them more often per round without consuming a bonus action, while Bonded Weapon uses up your bonus action, which also an opportunity cost, but only rally starts to matter later. I probably still would prefer the extra AC over the added range, especially in tier 1-2 where I only have one extra attack.
So, I think if it is important to set it off with other mechanical disadavantages. For example, you only have one arm -- that means you cannot hold anything in addition to your weapon, which may be a little bit of downside, but not that much. You still could use it as a shield, when you are not attacking with it, so no downside to AC2, and as an half-elf, you have darkvision, so no need to carry a torch or lantern. More importantly, treating it as an improvised weapon in the sense that you do not get your proficiency bonus to the attack is a real downside. You have to spend a feat on overcoming this, which is not a mean cost.
Overall, a point to hit is about as much value as a point of damage, and if you get d8 instead of d6 as with a javelin, this is about 1 point more damage on average. Not having proficiency is at least +2 less to hit. As I understand it, with your design you have an improvised weapon in the sense of not getting the proficiency bonus to the attack. I think that is not overpowered, compared to other options, and would not worry about proposing it.
1The rules for improvised weapons (p. 147f, PHB) say:
An object that bears no resemblance to a weapon
deals 1d4 damage (the DM assigns a damage type
appropriate to the object). If a character uses a ranged
weapon to make a melee attack, or throws a melee
weapon that does not have the thrown property, it also
deals 1d4 damage. An improvised thrown weapon has a
normal range of 20 feet and a long range of 60 feet.
So as a baseline using the normal rules, you can create this character with an Improvised weapon that deals 1d4 damage. And if you were an Eldritch Knight, you could have it return with your Bonded Weapon class feature. You would need to spend an ASI on the Tavern Brawler feat, so you also would be proficient with that weapon and get to add your proficincy bonus to the attack.
2 There is a SAC on this:
If you attack with a shield—most likely as an improvised
weapon—do you keep the +2 bonus to AC? Attacking
with a shield doesn’t deprive you of the shield’s
bonus to AC.