First you need to determine what is actively using this chimney? If their are furnaces Can they be switched to PVC vented? Water heaters to power vents or electric?
I had a chimney that had 5’ of bat guano in the bottom. Every rain it acted like a rain gauge and it got wet and stunk. Had no use for it since furnace was HE PVC vented now and wh electric. Took bricks off one by one ALL the way to under the concrete basement floor. Made closet bigger with space and eliminated a costly and reoccurring hole in the roof. I hate chimneys as a HUGE energy drain. All winter it is wide open. Do you let windows open all winter?
I would take out wet carpet and leave tile till you determine if it is wet and leaking. They make moisture testers if you need one. Could also check if rental stores have them? Maybe the flashing has now cured the leak. (WE HOPE). Check after EVERY rain cause leaks are tricky and wind direction sensitive. If it is raining inside and draining out research a better top that is rainproof.
Eliminating chimneys is a long term goal, preventing leaks a short term immediate need. Repairs ONLY after perm fixed.