I received unemployment for a few months in 2022 and then got a job. Will I owe addition taxes in 2023 due to unemployment?

I was on unemployment briefly in 2022, from January to April (I received it as back payment in April from when I lost my job in January). The value was a little over $2,000 and I opted to withhold federal taxes (I live in CA). Now I'm employed, and I'm worried that I'm going to get a smaller tax return because the taxes I withheld from unemployment won't be enough.

Last year there was an issue where the 10% CA withheld for unemployment wasn't enough, so we owed additional taxes despite opting to withhold them. 

The way unemployment works with a salary is very confusing to me. I already withheld federal taxes from unemployment, I don't want to owe more from my jobs salary or have my tax return reduced.