If you’ve created and using separate profiles for work and personal needs in the new Edge browser, Microsoft is making the Chromium Edge even better for you. New Edge already lets you open links in other profiles from the context menu, it even allows to choose and set a default profile to open external links through Multiple Profile Preferences in Profiles Settings, to manage the content between different profiles, the company recently has added and enabled Automatic Profile Switching setting by default. The setting is already available in the latest Edge Canary 82.0.449.0 and is rolling out to Microsoft Edge Dev as well.

As per Microsoft here is what this setting does: Automatic Profile Switching “detects links being opened in incorrect Microsoft account profiles and guides users to correct work, school or personal profile by showing a prompt that lets user switch to correct profile.”
For instance, if you’ve work and office profiles, Edge now ensures work-related links open in work profile and office-related links open in office profile, if any links open in an incorrect profile, Edge will ask you to move that link into a correct profile window.

You can also inform Edge which profile to use as default for external links, for this, visit ellipsis icon > Settings > Profiles > Multiple Profile Preferences and select and set Last used or one of the other profiles as default.
Note: Microsoft has announced about Automatic Profile Switching setting with Edge Dev 81 update, but that setting is still not available in the latest Edge Dev 82 build, maybe the feature could be still coming via controlled feature rollouts.
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