Yours is a complicated question because TM no longer backs up macOS itself (•) That means unless you have a very old TM backup of High Sierra, you would need to completely erase the startup disk and reinstall High Sierra from Apple's Recovery servers (or other legitimate source). Downloading High Sierra has become problematic, but there is this workaround that I have not personally tested:
High Sierra “The Recovery Server Could Not Be Contacted” Error. FIXED 2024
- Minor caveat: I am not certain that change coincided with Catalina. It may have been Big Sur. The change was so subtle it escaped my notice. In any event Apple's original Support document (archived here) was quietly changed to omit the option of restoring everything including the OS (current version here). In so doing Apple predictably followed the iOS model... no downgrades, period.
Next challenge: High Sierra may or may not be able to read that Time Machine backup, considering TM reformatted its backup disks to APFS, a file format HS does not recognize. Another quiet change that went unnoticed to all but seriously dedicated Mac aficionados.
Next challenge: Even if you can restore individual items from Time Machine, the data you want may not be readable by older software anyway. The more complicated the software, the less likely that newer data will be useful.
Summary: Given sufficient persistence and no small investment of time, I am sure you can reinstall High Sierra and use its (very outdated) version of Safari... but whether it's worth the effort is up to you.