I can't say i'm 100% positive, but nothing should be regenerating in your inventory over time. I've never seen this happening in my game. So if this is happening to you perhaps it is a mod. That being said, RDR2 does shower you with crazy amounts of supplies. Kill a few people and loot a few houses and you are basically stacked on items already and never have to use the shop unless you want something specific.
As for the ammo part, there are some conditions in the lootconfigdata that basically always give you ammo for looting people for your equipped guns, couple this with ammo drops in the loot tables and you basically never need to buy ammo. This settings can be disabled however, so that ammo is much harder to come by. In fact, you can remove ammo entirely from the loot tables and the config data to never get ammo from anyone. I did this for my game. The loot tables can be edited for basically all items you can loot from NPCs, containers, houses, and camps. You just have to edit these files on your own as RDR2 has no such settings to create a more hardcore game. Also, there are very few loot mods out there and none of them really scarcify the loot much.
Yeah this is a late reply, saw it as I was searching for something else so I figured I'd chime in just incase you haven't found the answer or anyone else comes looking.