Jigsaws make rather poor cuts (can use router afterwards but that's significantly more involved than a circular saw). Personally, I'd not use the jigsaw for pieces I'd hang on the wall, esp. not use jigsaw free hand. On hardboard - no direct experience with, yet I'd expect it doesn't like moisture, so it has to be properly sealed.

Jigsaw cuts look like garbage IME. The boxcutter knife would work, I've done that to trim plywood before and while it takes a while the cut is sharp and precise.

Better blades go a long way towards not splintering your workpiece. The Bosch ones are excellent if you get the "clean cuts in clean wood" ones. Note that there are two incompatible shank styles: T and U. Get the ones that work with your saw.

For sure. Couple other issues, one, the blade tends to wander, leaving not-perfectly-straight sections. You can mitigate by going slow and careful. Second, it needs a straight edge guide offset to the blade, which is harder to set up than direct.

All in all when I needed a one-off cut I used a box cutter knife, and when I needed a series I used a circular saw with a plywood blade. The setup is similar (needs an offset guide) but the cut is much straighter, faster, and less error prone. I think the only time I'd use a jigsaw is for making non-straight cuts like some curved artistic shape or something.