How can I specify the architecture (something like x86 or arm64) in Github Actions?
No you cannot set the architecture for the GitHub hosted runner. These VMs run x64. There is currently no way to specify or request another architecture.
If you need runners on arm64 or x86 you'll need to setup your own host/ VM and install the runner into it along with any other tools your build process needs.
You can use the GitHub/virtual-environments repo to borrow the setup scripts, but you'll need to make the proper adjustments to support the architecture of your choice.