What is the expected status update on paper return for 2022 tax year? I mailed my return on 4/6 but haven't heard anything since then

[xmasbaby0]

Until a human opens your envelope and enters information into the system, you will have to wait.  When they finally enter it, you can watch for information on the IRS site:

TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.

You need your filing status, your Social Security number and the exact amount  (line 35a of your 2022 Form 1040) of your federal refund to track your Federal refund:   

https://www.irs.gov/refunds

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund