Recharacterization of Roth IRA to traditional IRA then backdoor Roth IRA + 401K rollover

Timeline:

1. I mistakenly contributed $2236 to my Roth IRA in 2022 not realizing my MAGI exceeded the annual limit.
2. I recharacterized the full $2236 amount in 2023 as a Traditional IRA ($2223 actually got transferred), and then converted $2246 back to a Roth IRA in 2023. At the time of conversion, I had no pretax TIRA balance.
3. In 2023, I also did a rollover from an old 401K plan to my new brokerage account where some funds will roll into a Roth, and some will roll into a Traditional account.
   
   1. Keeping in mind the Pro Rata rule for the Backdoor conversion, I intend to roll these funds to my new 401K plan to keep my Traditional IRA account empty. 

I'm assuming in 2024 I will receive 4 1099-R's documenting:

1. Backdoor conversion from Traditional IRA to Roth IRA
2. Recharacterizing the Roth IRA to Traditional (this information will be documented in an explanation statement in my 2022 tax return).
3. Rollover from 401K to Roth IRA
4. Rollover from 401K to Traditional IRA

Questions:

1. How do I report this accurately on my 2022 return?
   1. I assume I enter the $2236 contribution to my Roth IRA on my 2022 tax return and denote that it's a recharacterization + provide explanation statement.
   2. For my 2022 return, do I also need to file a Form 8606 to report the $2236 non-deductible traditional IRA contribution? Given that the conversion happened in 2023, do I also report the conversion on my 2022 tax return? Do I report the 2023 401K to IRA rollover on this form?
2. How do I report this accurately on my 2023 return?
   1. I assume I enter information from my 1099-R to report the rollover back to Roth IRA.
   2. For my 2023 return, do I need to file a Form 8606 to report the conversion? Do I report the 2023 401K to IRA rollover on this form?