Your Question

I am playing on the latest version of the 1.21.1 mod, and I cannot change the max amount of trinkets any higher than 2, even after changing the chance to 100. There are other mods installed, but only QOL and loader ones such as Sodium. Nothing that should be interfering with Nameless Trinkets. I made sure to change my config, and my server config files, and neither are changing the max count

Currently, it's not possible to change it. You've probably updated from a previous version where the option was present in the configuration, but it isn't now.

It's also listed on the wiki.

https://nameless-trinkets.wiki/slots/

Currently the only way to add new slots is through the tools provided by Accessories mod.
Yes, I will reintroduce this option in the config in the future.