My brother is a finnish carpenter and I’ve done tons of finishing projects.
Fist off, the “sheen” is really personal preference. I like semi gloss, others like gloss and others like satin. It really depends on where it’s going, the lighting and more than anything, what you like.
As for what to use, well, you’re not dealing with “extreme” temperature. The inside of the keezer should really never go below freezing and the exterior is ambient. So long as it’s not kept outside you could use almost anything you want.
Oil based poly is great. Very durable, “warms” the wood but over time it “yellows” Some like the look others not so much. It’s more noticable with lighter stains.
Water based does not “yellow” but I’ve found it to be much less durable. It really shows any sort of water spots, drips, rings etc. I would not recommend it in most applications.
What I would recommend would either be laquer or Shellac.
Laquer is fairly easy to apply, either spray or brush and really durable. Shellac it “food grade” if that’s important but you are limited on the “sheens” also, they are often tinted.
Laquer of oil based poly is your best bet…IMO
Good Luck and post a pic when it’s done