Should I have received my tax refund by now? I sent it via mail March 22. Have not heard anything.

The IRS doesn't keep the refund website updated.  The IRS is taking a long time this year.  Plan on 6 months or more.  All you can do is be patient and keep waiting.

The IRS is still processing 2020 returns.  As of June 21, 2022 the IRS is almost done processing 2020 returns, filed in 2021.  See,

IRS continues work on inventory of tax returns; original tax returns filed in 2021 to be completed this week | Internal Revenue Service

And see

IRS Operations During COVID-19: Mission-critical functions continue | Internal Revenue Service

IRS Questions.  It says...

If you filed on paper, it may take 6 months or more to process your tax return.

Tax Season Refund Frequently Asked Questions | Internal Revenue Service

@luvm43786 - the IRS is woefully backlogged.  Assume that paper filed returns will take 6-9 months from the date it was inititally mailed in.

From the IRS website: 

As of July 15, 2022, we had 11 million unprocessed individual tax year 2021 returns. Of these, 1.9 million returns require error correction or other special handling, and 9.1 million are paper returns waiting to be reviewed and processed. This work does not typically require us to correspond with taxpayers but does require special handling by an IRS employee so, in these instances, it is taking the IRS more than 21 days to issue any related refund and in some cases this work could take 90 to 120 days. If a correction is made to any Recovery Rebate Credit, Child Tax Credit, Earned Income Tax Credit or Additional Child Tax Credit claimed on the return, the IRS will send taxpayers an explanation. Taxpayers are encouraged to continue to check Tax Season Refund Frequently Asked Questions.

How long you may have to wait: The IRS understands the importance of timely processing of tax returns and refund issuance. We have processed all error free returns received prior to January 2022 and continue to work the returns that need to be manually reviewed due to errors. We are continuing to reroute tax returns and taxpayer correspondence from locations that are behind to locations where more staff is available, and we are taking other actions to minimize any delays. Tax returns are opened and processed in the order received. As the return is processed, whether it was filed electronically or on paper, it may be delayed because it has a mistake including errors concerning the Recovery Rebate Credit and the Child Tax Credit, is missing information, or there is suspected identity theft or fraud. If we can fix it without contacting you, we will. If we need more information or need you to verify that it was you who sent the tax return, we will write you a letter. The resolution of these issues could take 90 to 120 days depending on how quickly and accurately you respond, and the ability of IRS staff trained and working under social distancing requirements to complete the processing of your return.

What you should do: In most instances, no further action is needed but you may check Where’s My Refund? or you can view your account. If you filed electronically and received an acknowledgement, you do not need to take any further action other than promptly responding to any requests for information. If you filed on paper, check Where’s My Refund? If it tells you we have received your return or are processing or reviewing it, we are processing your return, but it may be under review. If you filed before January 2022 and Where’s My Refund? does not have any information, your return has been opened but work on it has not begun. We’re working hard to get through the carryover inventory. Please don’t file a second tax return or contact the IRS about the status of your return.