How to get broken screw out of wall anchor
Those anchors are meant for drywall and use in wood may make them too rigid to accommodate the screws. It is also essential that the right size screws be used.

In general, anything but modest weight pictures or mirrors call for stud mounting, if possible. If not, toggle bolt connections, especially the newer strap style, are recommended.



I would remove the shelf, and back out those anchors. Restart with either screws in studs or toggles.