I filed my 2021 state and federal taxes by mail on 4/13/22. when can I expect to hear from them that they have been received and accepted?

Months and months from now it may be processed ... if you mailed it to the correct place then it will eventually show up on the IRS WMR? tool ... check once a week until you see it on the system :   https://www.irs.gov/refunds

when mailed you are never notified that it has been received or accepted unless you use a mailing method that has tracking. then you'll only be notified it was received.  if you're due a federal refund you can check the IRS website but it could be many weeks before the return gets entered into their system.

and the same for most of the states.