32-bit only apps don’t run, but apps that have multiple architectures, including 32bit, run on current macOS versions.
Example R-Name on Apple Silicon Sonoma 14.2.1
https://www.jacek-dom.net/software/R-Name/
mdls /Applications/R-Name.app | grep -A 3 kMDItemExecutableArchitectures
kMDItemExecutableArchitectures = (
"x86_64",
i386,
ppc
file /Applications/R-Name.app/Contents/MacOS/R-Name
/Applications/R-Name.app/Contents/MacOS/R-Name: Mach-O universal binary with 3 architectures: [x86_64:Mach-O 64-bit executable x86_64] [i386:
- Mach-O executable i386] [ppc_7400:
- Mach-O executable ppc_7400]
/Applications/R-Name.app/Contents/MacOS/R-Name (for architecture x86_64): Mach-O 64-bit executable x86_64
/Applications/R-Name.app/Contents/MacOS/R-Name (for architecture i386): Mach-O executable i386
/Applications/R-Name.app/Contents/MacOS/R-Name (for architecture ppc7400): Mach-O executable ppc_7400