Runecairn hits most of these points mechanically. Stamina is called fatigue and you can take as much as you have free inventory slots before it affects your attributes. Different weapons give you different fatigue causing dodges or attacks. Respawn at bonfires with non-souled enemies respawning. Collect souls and use them for recovery or increasing attributes. It's designed as as duet or solo game, and doesn't have the depth of lore that is a hallmark of souls-like games, but you could do it as an emergent lore, or pull from another source. It's explicitly a post-Ragnarok Norse setting, but sounds like you want more of a Dying Earth setting. Place the mechanics in Worlds Without Number's Latter Earth or the setting for Vaults of Vaarn (this might be more ruined Earth)? But I find any setting spun with the right atmosphere works better than trying to find a match.

There is also Grave, which is a souls hack of Knave 1e, but I haven't tryed it.