VA Loan to Refi Conventional?

Hello,

My fiance and I purchased a home in Nashville in November 2022. She did, my name is not on the mortgage, but it is on the deed. Her 30 yr interest rate is 7.29% for a $420K loan. We'd obviously like to refinance that mortgage and get a lower rate. I honestly didn't realize that using a VA Loan was an option to refinance through our current lender until I saw it listed on our lender's website. I have never used my VA Loan eligibility and, when I checked right now, my COE says that my basic entitlement is $36,000. So, question…can I use my VA Loan eligibility to help refinance our conventional loan? Is this a smart move? The ultimate goal is getting a lower interest rate locked in and lowering our monthly payment. Thanks.