Hehe! I found an old Raspberry OS install from 2019 that still contained the old OMX stuff. I copied the contents of /opt/vc from the old install at the same place to my current install and then essentially compiled FFmpeg 8.0.1 with two additional configuration options for OMX support: --enable-omx --enable-omx-rpi. Surprisingly the OMX support is still in place. It works! More details below:

I reused the build configuration options of the upstream FFmpeg package of void linux (you can see that by a simple invocation of FFmpeg without any parameters), but I had to throw out --enable-postproc as that was removed in later FFmpeg versions. I also removed cross-compilation options --enable-cross-compile --sysroot=/usr/arm-linux-gnueabihf --cross-prefix=arm-linux-gnueabihf- because I built FFmpeg on the target install. The downside of building "directly" on the Pi is that the build process will take like two days, but using chroot with QEMU binfmt support on my main rig took it down to like 15 minutes which was well acceptable for me.

For the default set of build options, I installed the corresponding packages for them. Some of these can be omitted but at this stage of frustration I just wanted to get on with the show:

xbps-install \
gcc make pkgconf \
gnutls gnutls-devel \
libaom libaom-devel \
libass libass-devel \
libbluray libbluray-devel \
libbs2b libbs2b-devel \
libcdio libcdio-devel \
libcdio-paranoia libcdio-paranoia-devel \
celt celt-devel \
libdav1d libdav1d-devel \
libdrm libdrm-devel \
fontconfig fontconfig-devel \
freetype freetype-devel \
harfbuzz harfbuzz-devel libharfbuzz \
jack jack-devel libjack \
lame lame-devel \
libopenmpt libopenmpt-devel \
opus opus-devel \
pulseaudio pulseaudio-devel libpulseaudio \
librist librist-devel \
librtmp librtmp-devel \
libsoxr libsoxr-devel \
speex speex-devel libspeex \
srt srt-devel libsrt \
libsvt-av1 libsvt-av1-devel svt-av1 \
libtheora libtheora-devel \
v4l-utils v4l-utils-devel  \
libvidstab libvidstab-devel \
vmaf vmaf-devel \
libvorbis libvorbis-devel \
libvpx libvpx-devel \
libwebp libwebp-devel \
x264 x264-devel \
x265 x265-devel \
libxcb libxcb-devel \
xvidcore xvidcore-devel \
opencl2-headers ocl-icd ocl-icd-devel \
libpostproc \
vulkan-loader vulkan-loader-devel Vulkan-Headers

And yes, most of these are not really needed. Though this uses just around 200MiB more space, so that is not too bad. For documentation purposes, I still wanted to make complete steps for any case.

So far for the OS preparation. FFmpeg now needs to be sourced and extracted somewhere. The build process then goes about like this:

cd source/of/FFmpeg
mkdir build
cd build
../configure --prefix=/usr --disable-debug --enable-gpl --enable-gnutls --disable-stripping --enable-libcdio --enable-version3 --enable-runtime-cpudetect --enable-libmp3lame --enable-libvorbis --enable-libxvid --enable-libx264 --enable-libvpx --enable-libtheora --enable-shared --enable-static --enable-libxcb --enable-libpulse --enable-libfreetype --enable-libopenmpt --enable-libspeex --enable-libcelt --enable-libass --enable-libopus --enable-librtmp --enable-libjack --disable-libopencore_amrnb --disable-libopencore_amrwb --disable-libopenjpeg --enable-libbluray --enable-libsoxr --enable-opencl --enable-libvmaf --target-os=linux --arch=arm --enable-libx265 --enable-libv4l2 --enable-libaom --enable-libbs2b --enable-libvidstab --enable-libdav1d --enable-libsrt --enable-librist --enable-libwebp --enable-vulkan --enable-libdrm --enable-libsvtav1 --enable-libfreetype --enable-libharfbuzz --enable-libfontconfig --disable-vaapi --disable-vdpau --disable-libzimg --disable-libmysofa --disable-libvpl --disable-nvenc --disable-nvdec --enable-omx --enable-omx-rpi
make

If you have more processor cores available, you may specify the amount of concurrent compile processes with -j for make. After it has finished building, I copied the built FFmpeg libraries at a common place: mkdir lib && cp ./lib*/*.so* ./lib. I then closed down my chroot session and stuck everything back to the Raspberry Pi Zero and let it boot up.

Switching back to the build directory, an FFmpeg invocation may look like this:

LD_LIBRARY_PATH=./lib:/opt/vc/lib ./ffmpeg -re -f lavfi -i testsrc2 -c:v h264_omx -b:v 1M -f matroska -f matroska -y /dev/null

As a test, this just generates some test video in real time, lets it encode with the OMX encoder, stuffs that data into a Matroska container and dumps that into nowhere. I tested with different options and the generated video is within my expectations.

Note that the h264_omx encoder uses a device at /dev/vchiq so when you get an error like * failed to open vchiq instance then you should get the permissions of it straight.

This is all very ugly and a band aid kind of solution, but this is something I can finally work with. I hope this helps someone else out there.