I’ve used the foodsaver with wet things, even whole wet fish. It might take a time or 2 but the bags do seal. They also make bags with an absorbent strip at the bottom. Or you could fold a paper towel strip and lay it along the bag opening just below where you will seal.
Please excuse me, I’m jumping in here without reading the other posts. What we do with wet foods is to first wrap the food in plastic wrap, then put that into the bag to be sealed. It has worked well for us.
If I’m doing really sloppy things, I’ll put them in a container in the deep freeze overnight, and then pop them out, put into the bag, and vacuum pack.
But we’ve never had a problem with fresh meats or fish. One of our first experiences was with a whole salmon we got a Costco; husband cut it into steaks, vacuumed a few to a bag, and they kept well in the freezer for many months.