A worm gear driven by a DC motor with an end stop to “home” at max height wouldn’t be overly complex (and likely cheaper/more reliable than a stepper motor and screw thread as the worm gear can’t be back-driven, so you can power it down and it will hold position to well beyond the tolerances needed for mowing).
If you just wanted to switch between a small number of pre-set heights (and changing those heights could be manual), a cam arrangement is probably better.
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A worm gear driven by a DC motor with an end stop to “home” at max height wouldn’t be overly complex (and likely cheaper/more reliable than a stepper motor and screw thread as the worm gear can’t be back-driven, so you can power it down and it will hold position to well beyond the tolerances needed for mowing).
If you just wanted to switch between a small number of pre-set heights (and changing those heights could be manual), a cam arrangement is probably better.