Whatever your final "fix" you might want to patch (& tape) the holes
first, so you have some tiny amount of structural integrity for the
kludges you insert. The screw-in plastic/pot-metal inserts are
potentially much stronger than the cheapo plastic anchors.

Going forward, understand that the wallboard has little strength- it's
in the framing. Learn how to find the studs and anchor stuff to them.

J