I have an external drive that for compatibility reasons is formatted as NTFS. All other applications don't have compatibility issues, but having the Thunderbird profile folder be stored on the NTFS breaks multiple things, saved passwords get reprompted every time, adding a new account does not make the account show up etc. How fix?

Forgot to mention that I am running on Ubuntu 24.04 LTS Thunderbird 128.0esr (64-bit)

There is no real cross compatibility between windows and Linux profiles. A number of things are still stored as absolute paths. You will always have issues.

However you forgot to mention the most important part of your setup relevant to this issue. Ubuntu 24 moves to snap packages and those are sand boxed. What local resources you have access to is strictly controlled by the sandbox. My guess is you only have read access to the NTFS volume from the SNAP. You will also see folk here unable to send mail, access their files to add attachments and any number of other minor and truly annoying inconveniences.

My guess is you will not have any issues if you install the Linux download from the Thunderbird site.