2FA problem no email with reset request

[Rafał Nowak]

I'm locked out of my Bitbucket Cloud account. The blocking 2FA is the Bitbucket-level two-step verification (legacy layer), not the Atlassian account 2SV. I lost my Authy app, so I can't generate codes.
What I've tried:
* Self-service recovery: triggered it, but the one-time login link has never arrived, well over 24h (checked inbox and spam).
* Org admin reset: admin went to Directory → Managed accounts → my profile → Two-step verification. There's no "Reset two-step verification" option; it only shows the org setting as "optional", and we have no Atlassian Guard. (Makes sense - the lockout is on the Bitbucket layer, not the Atlassian one.)
* Support chat: says they can't manually reset 2FA, keeps pointing back to the admin steps (don't apply) and the recovery email (never comes). They confirmed I'm not on any suppression list and the emails are being sent.
Questions:
1. When the lockout is specifically on Bitbucket-level 2FA and the recovery email never arrives, is there any path other than the emailed one-time link?
2. Can Bitbucket-level 2FA be reset by support or an admin when the managed-account panel doesn't expose it?
3. Anyone solved a case where the recovery email simply never lands - what worked?
Been going in circles for over a day. Any pointers appreciated.