There is an extension that can make externally opened links to open in temporary containers.

Not quite what you want but could work, depending on what’s your workflow and what you’re trying to achieve.

There’s also a software that acts like a browser and handles links, but instead of opening them, it shows you a list of browser’s you have installed and you can choose which one to use. It also has an option to open said links in private windows (incognito) instead of normal windows.

Again, probably not the solution you wanted, but works for me.

Of you like any of the two solutions I listed above, let me know, I’ll send you the links.