There are two taxable events. First, when your RSUs vest they count as income that you will have to report and pay tax on regardless of if you sell the shares or not.

Then, if you don't sell the shares you'll also owe capital gains tax on any profit between when you eventually sell and the value on the date they vested. Check with the broker to see how they account for the shares - FIFO (first in first out) or LIFO (last in first out) - or possibly, specific ID. You might be able to change that.

https://www.schwab.com/public/eac/resources/articles/rsu_facts.html#:~:text=Taxation,any%20state%20and%20local%20tax.