That's a really cool find and looks like it will make an excellent walking stick/cane!
Wood generally lasts a really long time, especially when not laying on the dirt and continually exposed to the elements. Does it need to be coated?
I would just finish (sand/scrape) the hand-hold area well enough to avoid splinters. It
might will wear and darken from skin oil/dirty hands, but that could be considered "character" that's added over the years. Especially after the user has passed - it becomes a family heirloom because of the wear.
I can see putting a metal cap on the base to protect it from splintering/crushing from the repeated banging into the ground with each step, especially if used on pavement. A small metal cup hand hammered to fit might work. My FIL would probably drill a hole in the end and run a small lag bolt in and use that. (Kinda kills the heirloom quality workmanship, to be fair.)
Maybe a rubber tip would be a better bet so it's not so noisy on pavement. A screw-in rubber foot might work well. I'd look for something that has a fairly easily replaceable rubber piece that goes into a fixed fitting. Drill a hole, squeeze in some epoxy, screw in the fitting. Buy a stock of replacement rubber tips now (products do go out of production), and present the finished work.