Is it permissible to take money left on the doorstep, and if its owner is not found, is it permissible to use it during financial hardship with the intention of returning it when funds become available?

What you found on the stairs is a lost item (Luqatah). You must announce it for a full year if it has value, and you are not permitted to use it before that. You can place an announcement near the building's staircase or inform its residents. If a year passes and you do not find the owner of the lost item, then you are permitted to benefit from it, while guaranteeing it to its owner should he come to claim it one day.