"zsh: bad CPU type in executable" and "mach-o file, but is an incompatible architecture" — what is the Mac actually telling me? Architecture

Same underlying condition, two different layers noticing it.

"bad CPU type in executable" comes from the system trying to launch a program. You asked to run an Intel binary and there is no translation available for it — usually because Rosetta is not installed.

"mach-o file, but is an incompatible architecture" comes from something trying to load a library into an already-running process. This one cannot be solved by translation at all: a process is either Intel or ARM for its whole life, and you cannot load an Intel library into an ARM process. The error politely names both sides — have 'x86_64', need 'arm64' means the file on disk is Intel and the process asking for it is ARM.

That second one is the one that bites Python users, because a native ARM Python is trying to import a package that shipped an Intel binary. There is no flag that fixes it. The package has to be reinstalled for the right architecture, or the whole environment has to run as Intel.

For question 2, three commands answer nearly everything in this room:

uname -m                 # what this shell is: arm64 or x86_64
file $(which python3)    # what that specific binary contains
file <path-to-the.so>    # the library in the error message

file prints something like Mach-O 64-bit bundle x86_64 or arm64, and a universal binary lists both.

The surprise for a lot of people is the first one. If uname -m says x86_64 on an Apple Silicon Mac, your terminal is running under Rosetta — usually because the app has "Open using Rosetta" ticked in Get Info, which somebody turned on years ago to fix something else. Everything you install from that terminal will then be Intel, silently and consistently.

That one checkbox explains an enormous number of these threads.