This is based on an excellent Stack Exchange answer by REJH (go there and give him an upvote).

Android 10 warning

It seems like this will crash apps if used on Android 10. See issue #2 for discussion.

Install without computer

1. Download an app that can copy a file to system directories. I used Root Browser Classic.
2. Download disable-direct-share.xml.
3. Enable root access for Apps in your device's Developer options.
4. Use the app to copy the file to /data/system/ifw/.

Install with adb

1. Turn on "Android debugging" in your device's Developer options.
2. Enable root access for ADB.
3. Make sure your device is visible when running adb devices.
4. Launch adb with root privileges: adb root
5. Download disable-direct-share.xml:

   wget https://raw.githubusercontent.com/stefansundin/android-disable-direct-share/master/disable-direct-share.xml
   

6. Install:

   adb push disable-direct-share.xml /data/system/ifw/
   

Uninstall with:

$ adb shell ls /data/system/ifw/
disable-direct-share.xml
$ adb shell rm /data/system/ifw/disable-direct-share.xml

Install with TWRP

1. Download disable-direct-share-v1.zip.
2. Download disable-direct-share-v1-uninstall.zip so that you can easily uninstall it at a later time.
3. Reboot into TWRP and flash the zip file. Do not use zip signature verification.

Magisk module

See this repository: https://github.com/AndroPlus-org/magisk-module-direct-share-disabler