[e2e] ensure user registration runs in a fresh session (#31164)
* [e2e] ensure user registration runs in a fresh session
* [e2e] align session key in Server Pro and SaaS
Co-authored-by: Antoine Clausse <antoine.clausse@overleaf.com>
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Co-authored-by: Antoine Clausse <antoine.clausse@overleaf.com>
GitOrigin-RevId: cc322217dc5a631c2795f477edaa90da8b83959e