macOS Catalina Time Machine backup won't overwrite

Hello and thank you. (2019 purchase.) iMac macOS Catalina 10.15.7 The Time Machine backup has started to fail with “not enough space” error … meaning it is no longer OVERWRITING OLD DATA as it should. Long session with Apple Support without success. They suggested FIRMWARE UPDATE. The G-TECH firmware I downloaded is not compatible with the latest macOS. I do not want to lose this backup data. Any suggestions? Thank you.