Currently, the trinket menu can only be opened from the vanilla or creative inventory (played on 1.21.1, so if nothing has changed, it’s still the same?), but there are also third-party inventory screens, like the Dragon Survival mod, which adds its own inventory screen where the button is missing. I suggest adding an option to configure in which inventories the button will appear.

@MrRain139 Such is a non-issue as of 1.21.4, since in any version or up you can declare the menu's internal id and accessories will attempt to inject a button into such a screen. Such a version even supports opening a mounts accessories screen like horses.

I am not planning any backporting at this time due to the amount of code changes, and more focused on providing new features rather than maintaining a bunch of additions for versions that are planned to be phased out with minecrafts constant development

I will close this issue for now, and if I decide to make a backport, I will reopen issues that would be helpful to track such