Create the backup
Open My List and select Create backup. Copy the complete text into a private note. It contains the saved title identifiers and valid manual episode checkpoints, not passwords or movie video data.
Merge in another browser
Open My List in the receiving browser, paste the complete text under Restore backup and choose Merge backup. Existing checkpoints there are kept. Recognised new titles and checkpoints are added, and the status explains what changed.
If the text is rejected
Check that the beginning and end were copied, without a note wrapped around them. Use a backup from this brand. Unknown titles and invalid episode reminders are not substituted with another production. Keep the original note until you have confirmed the list you expected.
Before clearing website data
Make a fresh copy first. Private tabs, another profile and another domain can have separate storage. Open My List to inspect the selections and checkpoints that are actually saved in this browser.