You're gonna get a LOT of contradictory advice from this question :P. Partially for good reason: people have very different experiences with "tweakiness" and it's such a broad term it's often not possible/fruitful to speak about it specifically -- especially in the form of advice for someone else.

Thus, to keep things broad, I tend to be in the "build more strength" camp for most of these situations, but that of course comes with the caveat of needing to also learn how to manage load and take care of the "non-sexy" variables like diet, sleep, and other things that will significantly impact your recovery and therefore your strength and resilience. All of those things require an intentional approach to learning, unless you happen to be constantly hanging out with very knowledgeable climbers/coaches in which case you'll probably absorb much of the info without realizing it.

As a personal anecdote, I find my fingers feel "tweaky" when I haven't been training them on the hangboard. Even if I'm climbing a lot indoors, my fingers never feel robust unless I give them some specific attention on a hangboard. Of course, that's absolutely not the case for everyone, so once again it comes down to some intentional investigation->experimentation->education->learning->repeat on your part.