What steps will reproduce the problem?

Reinstall towny

What is the expected output?

Expected players to do not have access to other towns, but they can open chests and break in towns.

Towny version

0.100.2.0, but the same issue follows me on 0.97.0.3

Server version

1.16.5

Please use Pastebin.com to link the following files

1. Your full server startup from the logs\latest.log: https://pastebin.com/2aF6FXy9
2. Your Towny config.yml: https://pastebin.com/EJT6X0L8
3. Your townyperms.yml: https://pastebin.com/zuna4pwG
4. Your log's error: no error logging

This is usually caused by Towny nodes put into a permission plugin. Did you put towny nodes into your permission plugin?

Yes, I did

I'd start by removing those. Adding anything like towny.* and towny.claimed.* has likely caused your issue.