Is it permissible to refinance loans with the same bank or with another bank to alleviate financial burdens, and how can one atone for previous Tawarruq loans?

The transactions mentioned, if they are an organized tawarruq (monetization) subject to Sharia-compliant regulations, or if you believe them to be permissible, then there is no objection to them. Otherwise, you incur sin.

It is not permissible to reschedule or sell debt unless the financing transaction is with an Islamic bank, such as tawarruq, in which case you settle the debt with the first bank and remain indebted to the second.