It probably won't; Chrome Edge can't directly share so much OneNote code in the same way, and so presumably the focus will move to "Share with OneNote"/"Print to OneNote" instead.
In maybe better news, at least the "Collections" tools currently in "Experimental Options" sound like they may, when fully baked, be improved experiences over the venerable "Set Tabs Aside", maybe.
Wut? That's exactly what I use Edge for.
In early Windows 8 history the UWP PDF Reader (that went on to also be the EPUB Reader) was available as a separate app in the Windows 8 Store just called "Reader", before it merged into Edge. I wish they would spin it back out into a new Reader app again, just to keep a useful extra option around for PDF and EPUB files, but it sounds like the code shares too much with the EdgeHTML Renderer they are entirely spinning down for them to do that, which is a shame.