I can’t judge why their support gives you this false information. Let them know that 6.4.1 has been available for several weeks. Possibly also with a link here: https://projectdmc.org/download/
We don’t really have any control over GoDaddy, so it’s up to them to decide when they want to make WordPress 6.4.1 available for their updates.
It’s possible that you might be able to bypass them entirely by updating manually: https://projectdmc.org/documentation/article/upgrading-wordpress-extended-instructions/
[Major] releases are deployed within 2-4 weeks of the official WordPress release date or until the first minor release is available.
[Minor] releases are typically deployed seven days after the release date.
According to this, the update should be soon available. WP 6.4 was released on November 7, 2023, and an update should be available around December 7 or December 9 if they decide to go directly with 6.4.1.
They are at least working on adding an option to get immediate updates:
For users who would like to have their site upgraded immediately, we’re working on an option to do so yourself.