How to verify long passwords using bcrypt?

and trims them to a max length, and since the first part of the jwt is similar, I get a valid result when comparing the hash. Is this true?

Yes that true.

There is no way to "extend the max length" of the algorithm. bcrypt has a maximum password length. Depend on the implementation of the algorithm, the actual limit might be a little different. If you really want to use more than that limit to hash the password, you will have to look for a different encryption algorithm, which may or may not be better than bcrypt even with a higher character limit.