Gitlab stopped processing 2fa resets for free users: GitLab Support is no longer processing MFA resets for free users
2FA documentation: Two-factor authentication | GitLab
which has the steps for resetting. If you had been running your own gitlab server, you can remove the 2FA from the Admin panel for the particular user. Unfortunately you cannot do that on gitlab.com. Which leaves only the 2fa_recovery_codes option to generate new codes. But as you don’t have ssh you cannot do that.
There are posts on here where I recommend using Authy as the app for your 2FA because this app has backup functionality, which means you can restore the app to any phone using the details when you set it up. That means losing a phone doesn’t stop you getting into your account. On new phone, install authy, restore, and then you have access to 2FA again. I can even run the authy app on multiple phones and if my battery dies in one, then I can use the other one.
Even if support would take your request, you cannot make it on behalf of your user. The user themselves would have to do it.