With the $16,000 2022 Annual Gift Tax Exclusion does the recipient pay any taxes?

The annual gift tax exclusion applies separately to each recipient. In 2022 you can give up to $16,000 each to as many people as you want to, and you will not have to file a gift tax return.

As tagteam said, the recipient never pays tax on a gift, no matter what the amount is.

The "gift tax exclusion" means that a gift tax return (IRS Form 709) need not be filed if the total annual gifts to a recipient do not exceed that amount.

The exclusion is applied per recipient.  If you give each of 4 individuals $16,000 (2022), the exclusion applies to each gift.

The responsibility for filing a gift tax return - when required - rests with the donor, not the recipient.

For 2022, the lifetime gift tax exclusion amount is $12.06 million.  No gift tax is actually due unless the donor's total lifetime gifts exceed that amount.  The purpose of Form 709 is so that the IRS can track your lifetime gifts.  Obviously for most people the gift tax return is for informational purposes only.