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.

However, they say:

> The Sovereign Tech Fund invests in open digital base technologies that are vital to the development of other software or enable digital networking. We invest in projects that benefit and strengthen the open source ecosystem. Examples include libraries for programming languages, package managers, open implementations of communication protocols, administration tools for developers, digital encryption technologies, and more. (...) We are currently not looking for user-facing applications, such as messaging apps or file storage services. If this changes, we will announce it here.

So, a browser wouldn't qualify, but an HTTP(S) library does, and perhaps even a browser engine would..?

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.