Thanks for the report. To find out why the second profile is missing, could you check two things in the Chrome profile that does not appear?
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Which account is the AgentsRoom extension signed in with in that profile? If you used "Continue with Google" there, it signed in with that profile's own Google account, which can be a different AgentsRoom account from the one your desktop app uses. Agents only see the browsers signed in to the same AgentsRoom account as the desktop.
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Open the extension popup in that profile, Browser tab: what does the line under "Let my agents drive this browser" say?
Also make sure the extension is enabled in chrome://extensions in that profile, and that a window of that profile is open when your agent lists the browsers.