You can attempt to manually install (sideload) the last compatible official APK version, though these often trigger unskippable "Update YouTube" prompts.
Technical compatibility
The YouTube app for Android 5.1.1 is available in various versions, with updates released regularly to fix bugs, improve performance, and add new features. Some of the notable updates include:
Immediately go to the Play Store, search YouTube, tap the three dots in the top right, and uncheck "Auto-update." Otherwise, your phone will try to install a broken version overnight.
This version introduced several features that defined the modern mobile YouTube experience, though they look archaic by today's standards.
Do not waste time trying to hack the official app to work. It is a losing battle.