When it comes to ELF, two accompanying debugging formats are overwhelmingly popular
The STABS format has not been used by default by any current compilers on ELF platforms for the last 10 years. It's definitely not "overwhelmingly popular".
The way to tell:
readelf -WS ./a.out | egrep '\.(stab |debug)'
You will see .stab section if the binary has STABS. You will see .debug_info, .debug_line, etc. if you have DWARF. You'll see nothing if you don't have debug info at all.
preferably without having to inspect section names
Can't be done without looking at sections: it's the presence or absence of these sections that makes the binary contain or not contain debug info.