Hello, I have switched my server to Forge. I installed the mod, but I literally appear naked for tlauncher players. I have even put the server in vanilla and it doesn't work.

DO NOT use Forge 1.16.5 in TLauncher, install forge manually and DO NOT change your .json file.
That prevents from using TLauncher Skin.

Remind, pirating is bad!

for tlauncher players

Is this a mod problem? TLauncher (more precisely, its fake from tlauncher.org) has such a problem, and it concerns not only OfflineSkins. Convince your players to use the original TL Legacy from tlaun.ch – it has no such problem.

tlauncher has it's own skin system and mod called tl_skin_cape (installed automaticly if tl_skins enabled). To remove tl_skins you need to disable it in launcher (account settings -> use tl skins -> false) or change some json files in your version (1.16.5) of minecraft (see the guides in internet): tl_skins: false