For the loan that was paid off, if it was paid off in 2023 with the refinance, depending upon what month that happened in, you should have received a Form 1098, Mortgage Interest Statement. The mortgage interest (and property taxes if you impounded this with your loan) on this form would be reported as part of your deductions and credits and would only be deductible if your overall itemized deductions exceed your standard deductions. Please see this link for guidance on how to enter this information in your return.
In regards to your refinance, it doesn't sound like it was an actual refinance since the proceeds were not for the same property but were for another rental property. A refinance would have been used to pay off your old loan and then used to finance the same property with different loan terms.
In regards to the new loan, if it was used to purchase a new rental property, please see this FAQ as you may be able to deduct more expenses than you would for your personal residence. The interest that is deductible will depend upon the terms agreed to when you signed the forms for the new loan. I recommend either contacting the agencies you are making your payments to as they should have also issued you a 1098 form. Any mortgage interest paid on the loan for the rental property will be deductible on Schedule E and included in your overall tax calculations.
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