LTR of 2 years? Dude, she's trying to behave well, and looking for other ways to behave well around you/for you. Give her a way to win by giving her something to do that you can reward positively.

Pay your bills. Suck your dick. Cook a meal. Whatever you need/want that could help you that you'd smile big and reward her for, that's what you tell her. If it's a trap and she berates you for the things you requested, your frame and relationship is weak, but this is exactly the kind of thing you should be working towards.

2 years? Oh man, throw that nice girl a bone already. You probably already know girls never want full disclosure, but if she behaves THAT well, let her feel a nice dose of that sweet security and commitment by opening up a calculated bit.

She now wants to know "one thing she can do (or do more of) that would show me she loves me".

Rim you out while giving you a blowjob. Just trust me on this. /lulz

You probably already know that you should NEVER let her know who you really are and should always be mysterious in a way. She's like a little kid that can't wait to open a christmas gift - super hyped at the beginning without knowing what's in it, once opened it's all clear what it is, she's fine with the toy or w/e, plays 5 mins with it and gets bored sooner or later.

She now wants to know "one thing she can do (or do more of) that would show me she loves me".

She literally invites YOU to tell her what she can do to please you. Don't overthink stuff like that and have fun from there.

Good advice in the comments so far. I'd say you're in a great position. You don't have to go all out revealing yourself. Just tell her something she could do. Or do more of. That'll make her happy.

Always show more over time as she earns it BUT never give her your whole heart (full disclosure)

My question is whether this innocent sounding request is really just another (un)conscious betatizing manipulation?

Yes. She's looking for the chink in your armor. Now it's not necessarily a bad thing. Girls need you to have this one or couple minor flaws that give them hope to eventually be able to exploit you. See https://heartiste.wordpress.com/2009/01/29/vulnerability-game/

So far, I've done OK with being vague and stoic with conversations about me, but I wonder if she'll ever get fed up with never getting a clear answer.

And that's the reason for the need to show that chink, even if it's a fake one, or a very minor one. If you're 100% alpha, she just might give up on you because she feels she'll never lock you down. She wants you to be 99.9% alpha. That 0.1% vulnerability is important for her.

Ignore her requests. She doesn't know what she wants. Your mysterious side is what keeps her attracted to you. As soon as you give up all your secrets you will be boring and your relationship will suffer.

reward her by telling her things about yourself, but maybe make it into a story and have roller coaster of emotions.