Erasing/reformatting is the surest way of a successfully removing all content and starting a new.
Simply deleting Time Machine database, can lead to issues of items getting stuck in the trash bin and no way to remove them.
Merging the partition is another issue.
Partition a physical disk using Disk Utility on Mac - https://support.apple.com/guide/disk-utility/partition-a-physical-disk-dskutl14https://support.ap
ref:
https://support.apple.com/guide/disk-utility/erase-and-reformat-a-storage-device-dskutl14079/mac
https://support.apple.com/mac-backup
3-2-1 Backup Strategy: three copies of your data, two different methods, and one offsite.
Boot clone https://discussions.apple.com/docs/DOC-10081
How to use Time Machine to back up or restore your Mac: https://support.apple.com/en-us/HT201250
Use DiskUtility Restore feature https://support.apple.com/guide/disk-utility/restore-a-disk-dskutl14062/mac
note: >System Preferences>Security & Privacy >Privacy>Full Disk Access
unlock the padlock, press the + button and add Disk Utility