Because I have not been keeping Pocket up to date, the Dropbox API is no longer syncing. You can still use Pocket, but it just will not sync. You can also still access all your data saved on Dropbox with the desktop version, which just reads the file locally on your computer. Here is the link in case anyone needs it:
You can export your data from Pocket under Config>Export. As for importing this information into another password manager, I think it depends on which password manager, whether they will be able to automatically read the Pocket format.
Thank you to all those who used Pocket.