I might just try LineageOS 18.1 and update it with a droid 10+ distro first.
You can get Android 10 (and newer) on the older Samsung Galaxy Note 10.1 (GT-N8000/N8010) via custom ROMs like LineageOS, with unofficial builds for Android 10 (LineageOS 18.1), 11, 12, 13, and even 14 available, providing a new lease on life for the tablet, but it requires flashing custom recovery (TWRP) and ROM files, so proceed with caution.
Key Points:
Official Support Ended: Samsung stopped official updates long ago for the Note 10.1, which originally ran Android 4.4 KitKat.
LineageOS is Key: Community developers maintain unofficial LineageOS builds, extending its life to modern Android versions.
Android 10 (LineageOS 18.1): Builds for Android 10 are available for the Note 10.1, bringing new features and security.
More Recent Options: You can find even newer unofficial builds (Android 12, 13, 14) on the Wikipedia page for the Note 10.1, though stability can vary.