Is this change to the Protection fighting style balanced?

I think a better comparison of the ability rather than shield is the dodge action (without the dex save bonus). Reworking the ability shifts dodge from an action , into a reaction, and requires it to target an adjacent ally.

Compared to say monk's ability to take dodge as a bonus action by expending their ki points. This seems rather powerful. As the monk ability uses limited resources, and uses a bonus action (which for monks is almost always used, where reactions are less so).

Also it doesn't really change one of your initial complaints. It might do nothing. If one creature makes a single attack against the target, it is effectively the same as before, and you have used your reaction.

So you end up where in some situations its extremely powerful. For example, following the leader in a narrow corridor. In which all attacks are now at disadvantage. And you end up where is effectively the exact same. Another issue: the Protector could use it, and the Protectee run away and still benefit until the Protector's next turn, which makes little sense thematically. So at the very least additional wording is likely needed.

Mathematically your change alters the effectiveness of the ability by 0%-500%+ (as 6 attacks in a round against a target isn't unheard of). It creates a wild variance in the effectiveness of the ability based on the situation. So any judgement on if it is "overpowered" depends entirely on how well the players exploit the new power. (for example two fighters could each take it, and watch each other so effectively the entire campaign attacks against them are at disadvantage)

Conclusion: The new power has potential to be abused/overpowered.

Suggestion:

I would suggest a different change. Allow it to be used AFTER seeing the attack, but still only affect a single attack. This means every single time you use the ability, you will at least be forcing a reroll of what you KNOW would have hit. So it would be more meaningful, however it would still only affect a single roll in a round, so it would not be a significant power jump.

Going off the premise that disadvantage is similar to a -5 penalty¹...

Your comparison makes it pretty clear

...act a bit like the Shield spell...

The Shield spell is a 1st-level spell available only to a subset of casters. It:

• is available at 1st level
• take a reaction
• grants a +5 to AC for all attacks
• uses a 1st-level spell slot (or optionally higher for no benefit)
• targets self
• lasts one round of combat

Your new style:

• is available at 1st level
• take a reaction
• grants disadvantage to all attackers
• uses no resources
• targets anyone except self
• lasts a variable amount of time

You are basically granting a Fighter something akin to the Wizard's 18th-level Spell Mastery

At 18th level, you have achieved such mastery over certain spells that you can cast them at will. Choose a 1st-level wizard spell and a 2nd-level wizard spell that are in your spellbook. You can cast those spells at their lowest level without expending a spell slot when you have them prepared.

With the difference of it can affect anyone except the caster, and it's duration is not fixed. The Fighter can use their reaction right after their turn for almost a full round of protection, or right before the Fighter's turn for something quick.

There is nothing stopping the Fighter from just invoking this every round of combat with the trade-off of losing AoO.

I think this makes the style a little too over powered.

¹ Here is one of many posts where disadvantage is mathematically close to a -5 penalty.