The credit allowed will be the lesser of the tax paid to the other state or the tax which Connecticut imposes on the resident's out-of-state wages." means that if you owe CT $4,000, but you owed the other state $6,000, your credit would only be $4,000 as CT is not going to give you a refund for the amount you paid to another state, but you can eliminate what you owe to CT with what you paid to the other state.
With the numbers you posted you would need to file a return, however, if CT taxes are $8,050 and NY is $8,000, you will owe CT $50. So you wouldn't need to make estimated tax payments for the $50.
You can walk through your TurboTax CT return to see what you would owe for 2021 without the credit which will likely be the same as the amount you would owe for 2022.
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