An idiot level expensive mistake.

[Straight Shooter]

Good of you to tell us NR hind sight is a wonderful thing !

When constructing stud partitions , think ahead in a kitchen area noggins could have been set at a predetermined height to hang the brackets.

There are other fixings for plasterboard...... butterfly clamps pre,drill hole slide the sprung loaded clamp through the hole (you would have to feed the bolt through the bracket first ) when clamp is pushed through it will spring out the butterfly arms you just tighten up.
Plastic butterfly raw plugs.....similar to a clamp but pulls the plastic arms against the plasterboard.

Metal cast self drilling raw plug ...large screw worm ...as you drive this in it cuts and tightens itself into the board ...in the centre it has a screw port for the screw fixing.

The screws for these brackets are standard 2" 10 s more than enough .

so when things go wrong for you ....tell us like NR .....we all learn something ....the very purpose of this forum.