I think the rules say you recover half your ammo spent if you search after a battle. That's too much of a pain to do in a tabletop session, but a game could automate that so after a battle concludes, you get a little line in the log which says "Recovered X arrows from searching the area" and get half the shots you spent back.
That said, I don't particularly care either way whether there's ammo taking up weight or if there's infinite ammo, just as long as it's not a big distraction from playing the game.
Limited-use crafted or enchanted arrows can be done without needing a limited supply of arrows, DOS 1/2 have infinite normal and craftable, limited magic arrows.
- The inventory shown in the demo was from a pre alpha version. They took lots of stuff from D:OS2 as placeholder. I do not know if we will get limited inventory slots.
PS:
Does PnP have limited inventory slots or are you only limited by weight?
DOS 1/2 had a weight limit, but everything took one inventory slot. Pen and Paper says what the capacity of a backpack is, but enforcing that depends on the DM and players, so if they don't want to spend their limited hours every few weeks micromanaging their inventory, they probably aren't too fussy about that.
Diablo has a tetris-style inventory, but the capacity for what you can carry on your person is absurdly large, so a tetris inventory isn't much of an indication of realistic carrying capacity either.
Essentially, micromanaging inventory isn't very interesting, so it tends to be streamlined or ignored, and that's not a bad thing.