This niche use case which offers a marginal benefit even to those who want it, is a laughable mask for the assembly and deployment of one of the world's largest data harvesting networks, the browser 'sync' account
Linkding is great, and has some browser extensions to inject your favourites into relevant search pages on the likes of google, ddg, bing, etc, which was a nice idea I hadn't considered before
You value the syncing browser accounts offer. Personally I like being able to go between several of my own computers and not have all settings synced. It's not a fresh slate situation but it is a bit freeing to not carry all my digital baggage all the time.
What about bookmarks that I don’t necessarily want to be publicly known. Not even talking about anything potentially embarrassing. Things like where I bank or my doctor’s appointment booking page.
Presumably that's a small set of bookmarks which you could manage across devices.
Other options might be to have that personal homepage on a non-public machine (e.g., on your home or office LAN), behind a VPN, and/or password protected.
Another practice from days of yore was to export specific bookmarks and transfer those to other systems. This is indeed cumbersome with mobile browsers (I'm not sure these even offer bookmark import/export ... Looks as if that's synch-only for Firefox/Android, which is disappointing.