Be aware that you recharacterized $6,000, not $5,200. $5,200 is the loss-adjusted amount transferred, not the amount recharacterized.
Your 2021 Form 8606 will show $6,000 on line 14 that will carry forward to line 2 of your 2022 Form 8606 to be added to your nondeductible contribution shown on line 1 of the 2022 Form 8606. This sum will be used in calculating the taxable amount of your 2022 Roth conversion.
