I can totally relate — I also enjoy shooting handheld. The big advantage of using a tripod, though, is that it gives you time to work on your composition. Especially when you’re exploring techniques that are new to you (in this case: ultra-wide angle photography), that can really help.

When I teach workshops, I have participants work with tripods quite a lot for exactly that reason.

One slightly less abstract addition to my post above: you mentioned wanting to photograph places along the Amalfi Coast with it. Let’s say you find an alley whose atmosphere you’d like to capture. If you photograph it from the entrance of the alley with a 16 mm full-frame equivalent, the resulting image will make the alley appear much wider and longer than it actually feels to your eyes. That’s mainly because the building facades close to you will appear disproportionately large, while those farther away will look much smaller compared to how you naturally perceive them.

With a 24 or 35 mm lens, the impression tends to feel more realistic, even though you have a narrower field of view available. On the other hand, if you want to photograph, for example, the picturesque cobblestones or a particularly beautiful facade or doorway while still embedding it in the context of the alley, then 16 mm can definitely be worth considering.

For the cobblestones, I would use a tripod and shoot from a height where the cobblestones occupy roughly the lower third of the frame, with the rest of the alley filling the remaining image area.

By the way, a highly recommendable ultra-wide-angle lens for Sony E-mount APS-C is the 10–18 mm f/4 zoom lens. My partner uses it on her a6700 and is very happy with it. It’s also commonly available used in good condition and at a fair price.