It is indeed a pity that this isn't listed anywhere in Settings, not even in Developer Options. The minimum-change way to get the information is as follows:
Turn on Developer Options and USB debugging
This is familiar, and this answer isn't the place to reiterate that.
Ask Android's Linux kernel
adb shell uname -m
The reply will tell you what architecture the Linux kernel in your Android OS is running. It tells you this in Linux terminology, rather than Android ABI names:
- "aarch64" is 64-bit ARMv8-A, which is Android's "arm64-v8a" ABI.
- "armv7l" is 32-bit ARMv7-A, which is Android's "armeabi-v7a" ABI.
- "x86_64" is 64-bit x86, which is Android's "x86_64" ABI.
- "i386" or "i686" are the basic 32-bit x86 or the Pentium Pro variant respectively, which is Android's "x86" ABI.