[CAL-3163] Add a flow in e2e that tests profile page to booking page for an event-type of an existing user that's invited to organization

[hariombalhara]

1. teampro outside the organization is invited to Acme and becomes teampro-example in Acme organization.
2. Go to teampro profile page. That would be acme.cal.local:3000/teampro-example
3. Navigate to any of the events of Team Pro. It should correctly navigate to the event instead of like taking to 404 page that happened in fix: Old username link on org user's profile. #13753

_{From SyncLinear.com | CAL-3163}

[hariombalhara]

This is still valid. Updated the description better.