The $3,000 limit is the amount of capital loss carryover that can be used to offset ordinary income. There is no limit on how much of the carryover can be used to offset capital gains.
For example, suppose you have a $20,000 capital loss carryover from 2021 to 2022. If you have a net capital gain of $5,000 in 2022, $5,000 of the capital loss carryover will be used to offset the capital gain. In addition, another $3,000 of the capital loss carryover will be used to offset other income (assuming that you have at least $3,000 of other income). So in this example, a total of $8,000 of the capital loss carryover would be used in 2022. The remaining $12,000 would be carried over to 2023.
Strictly speaking, it's not really correct to say that the capital loss carryover "can" be used in a certain way. Saying "can" makes it sound like it's optional. There is no choice about how a capital loss carryover is used. The calculations must be done in accordance with the tax law, and there is only one way to do it. The capital loss carryover must be carried from year to year, and it will be used as specified in the tax law.
