G29 is a code with a suite of functions to initiate leveling procedures like mesh readings; while the M420 is the G-code for setting or getting the bed leveling state in Marlin firmware.
Some of the M420 codes seem to overlap, but as long as you save to EEPROM, you can use G29 for the majority of what you need to do.

Just be aware that doing a G28 after activating a mesh will cancel a mesh unless you have your firmware set to reactivate it after G28 probing.