If my employer sold shares of my RSUs to cover taxes, do I need to pay taxes on them as if they were income? They are listed on my 1099-B

Yes. You may need to adjust your basis. Sometimes the 1099-B has the correct basis but you need to verify that the amount included in your w2 box 1 per share was added to your 1099-B. If not, you need to adjust the basis.

The sale was used to cover all the necessary taxes.

For example: You received 500 shares for $xx dollars and 30 shares were sold to cover taxes.

Your w2 box 1 has the income for 500 shares. You should have a statement with the price per share.

30 shares were sold and that w2 part  is added to the basis - unless the 1099-B is accurate (sometimes it is).

Be sure to keep a copy of your w2 and sales like this in a financial notebook. Keep it safe and each year, add your year-end statements from all your financial accounts plus a copy of your W2’s, your  carryover information, and proof of your basis in your various investments. You must keep tax records  from the time you purchase until sold/ loss used plus 3 years. It is very easy to lose track of disallowed losses, carryforwards,  and basis. This can be a digital or paper notebook.