It seems like you've logged in with your personal email account. In order to use Google Cloud's Solution Explorer, you'll need to switch to a Google Workspace account.
If you don't have one, you can create one here. Alternatively, you can ask your domain administrator to provide you with one, or to implement Workspace Identity Federation.
Converesly, you may continue as a guest by logging out of your current Google account or by opening Google Cloud Solution Explorer in incognito mode.