Starting from Magisk version 22, the Magisk (core) and Magisk Manager (companion app) files were merged into one package for your convenience. And one of the advantages of that was the new all-in-one package would also be a flashable zip file recognized by the TWRP custom recovery image.
However, it’s also true that you can get root access with Magisk without using a custom recovery image. Note that it’s very difficult to create a universal layman guide for this topic, so we generally advise you to search for a rooting tutorial for your device rather than a universal method without a custom recovery image. This is in part because installing the firmware aspect can vary between manufacturers. But the following are the general steps to root without TWRP using Magisk.
See also: How to Get boot.img for Magisk
How to Install Magisk without TWRP
Note: The way you install Magisk without TWRP is with a modified boot image. This is the actual boot image that boots up the operating system. There are some caveats to modifying the boot image. For instance, if you install future Android software updates, they will remove the modified boot image and replace it with their own standard boot image again, which means after you have rooted with Magisk, you want to turn off the software updates. If you turn off automatic updates in Developer Options, Android won’t bother you with notifications regarding software updates when they arrive.
1. First, unlock the bootloader. The procedure for this varies between manufacturers, so look up the correct tutorial for your smartphone’s model.
2. On your smartphone, download the latest version of Magisk.
3. On your computer, navigate to the path of your downloaded file—for instance: C:\ProgramData\RSA\ROM Files—copy the boot.img file, and transfer it to the smartphone. Use the Magisk app to patch the boot.img and it will create a new patched version of the boot.img file.
4. On your computer, download the android sdk platform tools (or just the minimal adb and fastboot), and copy the patched boot image to that folder so they are both located in the same directory.
5. Connect the smartphone to the computer in Bootloader Mode.
6. Type the following command into the command line and then press Enter to execute it:
fastboot flash boot patched_boot.img
7. The patched boot image will be flashed to the smartphone and you should be rooted with Magisk.
See also: What Is SafetyNet on Magisk
In conclusion, that is how to install Magisk without TWRP Recovery to get root access on Android.