The Backdoor Roth IRA contribution limit is the same as the IRA contribution limit for a given year, since you need to make a non-deductible IRA contribution to then convert it to a Roth IRA. The IRA contribution limit for 2022 is $6,000 per person, or $7,000 if the account owner is 50 or older. The IRA contribution limit for 2023 is $6,500 per person, or $7,500 if the account owner is 50 or older. So if you want to open an account and then use the backdoor IRA method to convert the account to a Roth IRA, that's the maximum you can contribute.
There is no limit on the amount of Traditional IRA (TIRA) money that you can convert to a Roth IRA or how many conversions you can make. At tax time, you total them and report just one conversion amount.
However, as the other reply said, there IS a limit on how much you can CONTRIBUTE to a TIRA, as the first step in doing a "back door" Roth contribution.
Can you recognize any stock losses with the back door conversion as well?
Q. Can you recognize any stock losses with the back door conversion as well?
A. No. Gains and losses on stocks held in an IRA (traditional or Roth) are not reported. All distributions are ordinary income. At one time, it was possible to deduct to deduct IRA losses, but only in VERY limited situations and only as an itemized deduction. But not under current law.
If you sell stock in order to make an IRA contribution, that would be reportable. But it would be separate from the "back door Roth".