The site make your 2fa stop working after you try to recover you send them proof like id, ip where you create it. date of creation.
coins you used and everything they ask.
and they still dont give you access back. I lost 1 eth.
Well, I don't know what your experience is like with the exchange, I've been a user of gate.io exchange since 2018, I have 2fa activated on my account and I've once been locked out of my account due to lost access to 2fa because I changed my phone and didn't have the correct back up code required to restore my account 2fa.
I contacted their customer care, this was way back 2020, I followed all the process I was asked to, it took some time, about a week or over, in the end, my account 2fa was resetted and I was able to login again and set up a new 2fa.
After the incident above, I learnt to withdraw all my funds on centralized exchanges to my non-custodial wallet before changing my phone or performing any thing that has to do with factory reset.