Hi,
- native open source drivers
- supports at least three monitors
- PCIe x16
- support for 4K
- HDMI output
- audio not necessary
AMD cards are going to be your only options here, because the two choices for open source drivers are AMD and Intel, and Intel doesn't make stand-alone cards with multi-monitor support. (With some laptop models, you can drive the internal display plus one with the built-in external HDMI plus one over thunderbolt, for a total of three displays, but that doesn't sound like what you're looking for.)
I personally have been very happy with AMD cards (previously, a Vega 56 and now a Radeon Pro W5700) on Fedora Workstation -- they basically just work, and provide a great gaming experience.
Those are in a completely different range from what I was thinking. $800 for a video card? And only using the open source driver?
That seems to be a typical price for a gaming video card.
I mentioned earlier on, but probably should have been more clear, that I'm not really interested in it for gaming. This is my everyday desktop that I use for a Windows VM and office work. Hmm... are these games on Linux that people are playing, anyway?
How about this card? It says it's on sale, but is it really? https://www.newegg.com/gigabyte-radeon-rx-5500-xt-gv-r55xtoc-4gd/p/N82E16814...
This has three DisplayPort connectors - my current monitors do support displayport, although I'll need new cables.
I did see one card online at the store I usually buy from. It's a Radeon™ Pro WX 2100 for $200CAD that supports up to 3 4K monitors. This isn't a recommendation because I haven't done any research or comparisons, but you might be able to find something.
Looks like about $140 USD on amazon here - but only 2GB RAM? Won't that affect the maximum resolution?