Are these Bracers of Blinding Strike balanced

From DMG p.187, the initiative is suggested as minor property to add onto a magic item to make it distinctive:

Guardian. The item whispers warnings to its bearer, granting a +2 bonus to initiative if the bearer isn't incapacitated.

Therefore, the sword is less powerful than a +1 sword and is suitable for a party of this level.

The cloak is not as good as Armor of Resistance (Rare) or Boots of the Winterlands (Uncommon) but better than a Potion of Resistance (Uncommon). It is probably OK but if you are worried you can make it require attunement.

By comparison to the pre-existing Instruments of the Bards, the first is balanced, the second may be slightly too strong but is probably alright

Let's compare your proposed spell lists to the pre-existing sets from the Instruments of the Bards of equal rarity:

Mac-Fuirmidh Cittern (Uncommon):

barkskin, cure wounds, fog cloud.

Fochlucan Bandore (Uncommon):

entangle, faerie fire, shillelagh, speak with animals.

Doss Lute (Uncommon):

animal friendship, protection from energy (fire only), protection from poison.

Koeth Flute (Uncommon):

feather fall, gust of wind, protection from energy (cold only).

None of the pre-existing instruments have any damaging spells at all, which is good for your proposed instrument as it also has none.

We can assume that the two protection from energy spells are roughly equivalent, so let's look at feather fall and gust of wind.

The first is a situational spell, in fact, it can only be cast as a reaction anyways. I would say this spell is situationally useful similar to fog cloud, faerie fire, and protection from poison, and isn't particularly strong compared to completely ending a current poison.

The second is a somewhat useful spell as it allows you to push enemies and cost them some extra movement, but when compared to entangle which has a much stronger effect (restraining), it seems balanced. I would say that entangle and animal friendship are both good "shutdown" spells, as they deter or limit their target much like gust of wind.

Conclusion:

The proposed instrument, aligns well with the pre-existing instruments and follows the slight pattern there as well. If anything, I would say it is weaker than the others, though not by much as the usefulness of the situational spells is very campaign-specific.

Cli Lyre (Rare):

stone shape, wall of fire, wind wall.

Canaith Mandolin (Rare):

cure wounds (3rd level), dispel magic, protection from energy (lightning only).

Naeris Viol (Rare):

enemies abound, pyrotechnics, heroism, thunderstep.

We can immediately see that your instruments provides more spells than the others, though this is not exceptional as the Fochlucan Bandore mentioned earlier also did this.

Healing:

I feel a good comparison to make is between cure wounds and heroism. The first heals for 3d8+MOD while the second gives MOD temporary hit points each turn that concentration is maintained. Assuming a modifier of +4 it takes 5 turns (not too long for a combat) for heroism to become better, and with a modifier of +5 it takes only 4 turns. Thus, I feel alright saying this spells are about equal, if not having heroism being worse as it takes longer, is not guaranteed due to concentration, and cannot restore a creature to consciousness.

Damage:

Your instrument then has a good damaging spell (thunderstep), though it does an average of 16.5 damage compared to wall of fire's 22.5 damage. Though fire damage is often resisted, wall of fire will often hit more enemies as you can define its shape better, and it does not require enemies to be near the caster. While thunder step also allows you to teleport, and get out of a tight spot, wall of fire persists (barring concentration) and can deal damage multiple times, detering (shutting down) enemies as well. This puts them about on equal footing, if not with thunder step being worse.

Shutdown:

Your instrument then gives two "shutdown" spells: enemies abound, and pyrotechnics. These can either turn an enemy against its allies, or blind an entire group. Though these spells are not particularly strong, and I often see a caster picking up dispel magic as it is the spell to shutdown persisting spells, which are often quite strong themselves. The choice is whether you want to shutdown an enemy or shutdown a spell. These seem about equal to me, though dispel magic has some more use outside of combat, the two spells provide versatility simply by having more options.

A problem:

This would have us comparing thunder step with protection from energy, where thunder step is quite often the superior choice. This points out what I feel the Viol does too well; it covers too many bases. Your instrument provides healing, shutdown, and damage (with a bonus escape tied in). Though it isn't particularly great at any of the three things, it does provide a lot of versatility for the user.

The Lyre provides shutdown (the walls) and damage (wall of fire) but not any sort of healing, compared to the Mandolin which provides healing (cure wounds), and shutdown (dispel magic). Your instrument provides all three.

Other Benefits

Note that both of the other instrument also provide a situational benefit (stone shape and protection from energy), while yours, at best, provides heavy obscurement (pyrotechnics).

Conclusion

Your instrument doesn't excel in any of these categories, so it is likely balanced, in fact, it is outdone in each category by one of the other instruments. What may make it slightly overpowered is simply the amount of versatility it provides with its spells.