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Just do multiarch builds, I do this all the time

The other option would be to let k3s use the system’s containerd instead of its own. So docker and k3s would rely on the same container engine.

I'm running an 8 node k3s cluster on RPi4, I actually use Google cloud build to build the containers if I don't build them on my local Linux VM. Dockerd has some licensing constraints containers doesn't. You'll run into the same issue with dockerd as with containerd, the container must match the kernel (windows or Linux, I'm assuming you're not running windows on the rpis though so Linux is a safe bet) and processor architecture (AMD/intel (intel AMD desktops, old intel macs) or ARM64 (apple M1 and m2, raspberry pi etc)

The final plan is to build and deploy Swift based projects on my cluster. I have some sort of Docker knowledge so I can write Dockerfiles. I learned that there are other ways to build and push images even into docker hub without actually using docker cli tools.

You'd need to use a builder of some description though. Docker is one way, but you can use podman (OSS) or buildpacks (CNCF ex-google). Google use bazel for their builds (I have never used it and seems to complex for most of my use cases). When I push to Google Cloud Build I am using stock standard docker. Github actions can also do the build for you (it'll probably use docker under the hood)