OP, I sympathize with you. You're being wise, not paranoid.
Being careful doesn’t mean you're subscribing to conspiracy theories as several suggested. Of course, Apple's not going to deliberately put in old batteries, especially not as a matter of policy. But all sorts of things still can go wrong in any given Apple Store, with any given tech, with any given repair, on any given day.
“Trust, but verify” is a smart policy.
Yet, apply it strategically. No need to take one's laptop into the AppleStore or be pushy demanding documentation, observation of replacement, or any on-site instant confirmation.
Just do a Coconut Battery check beforehand at home, taking a screenshot of the info about cycles and health — and, then, do it again when you return from the repair.
If there were to be an issue, which would be highly unusual and very unlikely, you have the needed evidence to return and request a fix. If it happens, you could also report the situation to the manager and to national Apple HQ.
In any case, to those who uncharitably and unfairly assailed the OP for being paranoid, do remember that
“Just because you're paranoid doesn’t mean someone isn't out to get you!” 😎