I currently use Chrome's account profiles for this, so I have a desktop where my work profile lives and a desktop where my personal profile lives, and this makes links followed from other applications Just Work so long as I'm on the right desktop for them. I could probably get used to a slightly more awkward workflow, and the history being annoyingly shared between them, but...
EDIT: ah, well, I found the relevant github issue. Looks like there's years of arguing yet to go! https://github.com/mozilla/multi-account-containers/issues/3...