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There's also a small amount of IO pins on a high density header. I built an adapter that converts the LVDS voltage levels to TMDS so you can use it with HDMI or DVI - https://github.com/teknoman117/ACORN-CLE-DVI
What exactly are you aiming to build? DP/HDMI output and Ethernet aren't exactly beginner topics in FPGA (though you may be able to cobble something together using pre-existing components).
The Nexsys Video would give you what you need: https://digilent.com/shop/nexys-video-artix-7-fpga-trainer-b... (though out of stock)
The DE10-Nano gives you both HDMI (though not 2.0) and Ethernet: https://www.terasic.com.tw/cgi-bin/page/archive.pl?Language=.... There's some availability, apparently buying direct from Terasic is the best option (though often more expensive as shipping is pricey and you pay import duties). It's also what the MiSTer project uses https://github.com/MiSTer-devel/Main_MiSTer/wiki so is what you need if you want to play with console emulation.
FPGA toolchains are indeed a nightmare but both Xilinx and Intel have freely available versions. They tend to be limited in the devices they support but the free versions of Vivado (Xilinx) and Quartus (Intel) both support the FPGAs in the boards I mentioned above.
A bit of a nitpick - LiteX still needs Vivado installed for now for 7 series FPGAs. There's a project that's very far along in reverse engineering the Xilinx bitstream (https://github.com/f4pga/prjxray), but it's still missing many features (PCIe, SERDES, etc.).
https://github.com/enjoy-digital/litex/wiki/Use-LiteX-on-the...
Not equivalent to the Pi 4, but still runs linux. (the Acorn CLE is a rebadged NiteFury)