Depending on how you define "global", https://www.sovereign.tech/programs/fund might qualify:

> With the Sovereign Tech Fund, we invest globally in the open software components that underpin Germany's and Europe's competitiveness and ability to innovate.

Not globally funded, but does invest globally.

There are several other programs like STF funded by the EU (often mediated via NLNet), and for example Servo gets some amount of its funding via NGI (an EU Commission initiative): https://nlnet.nl/project/Servo/

Edge exposes its engine to be used in other programs like Skype.

Edge no longer has its own engine, it's based on Chromium now. When it did, it also wouldn't qualify for STF funding because it wasn't open source.

But yes, a browser engine is potentially an embeddable library, so an open source one might qualify :)

You ever noticed how the majority of Linux desktop related companies are european?

That’s not an accident. So yes, there’s precedence

If we're talking about commercial desktop products, is it really a majority?

Canonical is UK-based.

I can think of Suse but even that changed hands several times through a bunch of US companies.

Red Hat/Fedora, PopOS, Chrome OS etc. all are not european

Not desktop companies, but related. Document foundation, for example.