FE 20-70mm f/4 G, I'll get this lens. 

Exactly what I was thinking

Noted!

Subbing for updates

Honestly, I am not 100% sure which exact focal length is gonna be your favorite, but I think you really gotta focus on the build quality and reliability for a one-lens travel setup. If your only lens fails in the middle of a trip, you are pretty much stuck, right??? IIRC some of the lighter lenses tend to compromise on weather sealing to save weight, which is kinda risky when you are out in the wild.

• Definitely look for something with internal zoom if you can find it, it basically keeps the dust and moisture out much better.
• Make sure it has a rubber gasket at the mount because that is a major weak point for the a7 III body if things get wet.
• I think I heard that some of the more affordable options have inconsistent quality control, so checking for a solid build is a smart move.
• Tbh, I would prioritize a lens with a constant aperture because they usually have better internal construction and are way more reliable in the long run. Traveling is pretty rough on gear lol, so dont just look at the image quality specs on paper. You wanna make sure it can actually survive a few bumps and some light rain without dying on you!!!

Been using this for years, no complaints

Tamron E-mount lenses are a good choice.