The $16,000 is the Safe Harbor, don't have to track it amount. You don't have to pay taxes on gifting more than that in a year, you just have to keep track of it until you reach the actual "free" gift limit of $11.58 million lifetime.
https://blog.taxact.com/gift-tax-do-i-have-to-pay-gift-tax-when-someone-gives-me-money/#:~:text=Gift...).
The person gifting files the gift tax return, if necessary, and pays any tax.
If someone gives you more than the annual gift tax exclusion amount ($15,000 in 2020), the giver must file a gift tax return. That still doesn’t mean they owe gift tax.
For example, say someone gives you $20,000 in one year, and you and the giver are both single. The giver must file a gift tax return, showing an excess gift of $5,000 ($20,000 – $15,000 exclusion = $5,000).
Each year, the amount a person gives other people over the annual exclusion accumulates until it reaches the lifetime gift tax exclusion amount. This lifetime exemption means one will not have to pay gift tax on further gifts.
As of 2020, a taxpayer does not pay gift tax until they have given away over $11.58 million in their lifetime ($5.49 million in 2017).
