Yes you will owe less tax or get a refund. Did you already file?
If you have filed. The IRS will recalculate your return for the new 10,200 unemployment exemption for you. There is no need for taxpayers to file an amended return unless the calculations make the taxpayer newly eligible for additional federal credits and deductions not already included on the original tax return.
See new article May 14, 2021
https://www.irs.gov/newsroom/irs-begins-correcting-tax-returns-for-unemployment-compensation-income-exclusion-periodic-payments-to-be-made-may-through-summer
If you have not filed, Turbo Tax is updated for the 10,200 exemption. You don't have to do anything special to get it. It is automatic. Just enter the full amount on your 1099G. Your unemployment compensation will be on Schedule 1 line 7. The exclusion will be on Schedule 1 Line 8 as a negative number. The result flows to Form 1040 Line 8.