If you filed a tax return properly and IRS claims to never having processed it, wouldn't anybody be concerned? You said the IRS got the payment and that : "IRS rep in 1/2022 told me she knew return was received by IRS because she could see it had been marked with an "IRS document number."" So they have it but it is just not processed ... balance due returns are on the very back burner in a very deep pile.
Additionally, other things that depend on tax returns, such as Social Security credits, are not reported because those agencies depend on IRS reporting the tax returns. For example, Social Security still shows no Social Security income for 2019, because IRS has not processed the tax return. Actually the income that is reported on a W-2 goes directly to the SS administration and then the SSA sends the info to the IRS not the reverse so they already have it ... check your account online with the SSA. So this actually may be where some of your issue lies ... did your employer file the W-3 timely ? Only Self Employment is sent to SSA from the IRS.
I would give this another 6 months and then if you don't see progress contact the taxpayer advocate office for assistance.
