My experience of being on the other end of this is quite old (2001-2002) but I doubt the fundamental dynamics have changed.

There are some things for which your representative absolutely has a fixed vote, either because they personally have a strong view or because political constraints (district demographics, internal party pressure, whatever) are significant. For other things, they will likely pattern match against their broad inclinations (for free trade, anti taxes, for green energy, whatever) at least as an initial position. For many issues, though, your representative probably doesn't care much at all, by default.

But the ways things move from the second or third boxes to the first are pressure (enough voters/co-partisans/whoever caring makes inaction politically expensive), money (election campaigns cost cash and so cash buys attention if not actual votes on legislation), or convincement.

If enough people write on some esoteric subject someone in the rep's office will notice, because tracking political issues is part of their job. Staffers help shape reps' policy positions and voting behaviour, at least in part because reps are too busy to pay attention to everything that comes up. And if the campaign is big and noisy enough that it threatens to become a major electoral issue then that will also force a decision one way or another. So it is possible to influence positions and behaviour, but not on every issue and very likely not if you're doing it alone (and don't write large cheques).

You'll definitely get a form letter for anything they have a form letter for, though. And even without then the actual letter is likely written by an intern or junior staffer (or I guess GAI these days). But then when I was reading incoming mail most of that was form letters and pre-printed campaign postcards too, so it was difficult to feel too regretful that the replies were mostly mass-produced rather than artisanal.