Near-term
Currently the user has to remember to switch to the Byterover extension tab to "authorize" Byterover for the current project. This should be easier on the user. The extension could ask the user something like.. "new project detected! Would you like to initialize Byterover memory for it?" This popup could offer Yes No Later buttons. If yes, Byterover should offer sane defaults for Byterover organization and project name and present that to the user (editable) with OK/Cancel. If OK, the extension should take care of the rest.
This way, a jump out to the browser would be obsolete and the experience much smoother
and
faster.
Long-term
Automate this completely. Let Byterover handle which space (user default?) and name (folder name of the project?). Add settings to the extension that lets users configure settings for this stuff.