In your case, I would assume that you're looking to actually use your iPhone 12 mini, after replacing the battery, as opposed to seeking out the actual trade-in value. Would it be worth it to you? Honestly, I suspect so. If you have a particular affinity for your mini, possibly because you just can't abide the larger form factors, then you're pretty much stuck with a 12 or 13 model, as there is no 14 mini and there almost certainly won't be a 15 mini; Apple has moved on from the smaller form factors. And given that an upgrade to a 13 would be a lot more money for a lot less relative value, I personally think you might reasonably find it worth the few dollars that it would cost to replace that battery.

Oh... but don't do it through Apple; do it through a reputable third-party. Way less expensive, and likely a lot faster.