Only interest on acquisition debt is deductible. Acquisition debt is debt used to buy, build or substantially improve the property. Interest on the equity debt is not deductible.
If we assume the original loan through June 2021 was all acquisition debt, that interest is fully deductible on schedule E against rental income.
For the refinance, you still only have $200K of acquisition debt against $300K total debt, so roughly 2/3 of the interest is deductible. As you make payments, you can consider that you are paying off the equity debt first. On July 1, if your acquisition to total debt was $200K/$300K, then 66.6% of your interest for July is deductible. By December 1, your ratio might be $200K/$290K, meaning that 67.8% of your interest for December is deductible.
Because the percentage of deductible interest changes each month, the IRS provides two ways to calculate the deductible portion. One method is to average the first and last month balances (in this case, your first month is July, but on your 2022 tax return, your first month is January, of course); the other method is to determine the percentage for each individual month from your statements.
I don't know how well Turbotax will calculate this for you, there are always a few complaints about personal mortgage interest (your residence), so the same issues may apply to calculation of business interest. You may just want to calculate it yourself and enter the final number.
And of course, if you use some of the equity cash to make improvements to the rental unit, that will increase your acquisition debt.
