One authorization connects the panel to your account. It then reads each project’s own API key by itself — there is nothing else to find or paste.
Click the extension icon. On first run the panel opens its Connect to Testomat.io screen.

The Choose a project screen lists your projects: search, click one, done. You can switch projects any time from the panel header.

A General token (Testomat.io → Account → Access Tokens) works in the same field.
Using your own Testomat.io server? Before authorizing, open Advanced and
put its https:// URL into Instance — the authorize button follows that
field. HTTP URLs are refused.
Settings → Connection shows the card: which host, the Connected badge, and the current project. Disconnect forgets the instance and returns the panel to the connect screen.

Normally you never see this. But when the panel loses its session — an old token, for example — it does not break, it switches to basic mode: runs, statuses and comments keep working, while finish run, priority, custom statuses and assignee switch off, and ticked steps stay only in the panel. A banner says it happened: sign in to Testomat.io in this browser, press Refresh on the banner, and the full panel is back.