Is Manganese Violet suitable as a food coloring?

As absolutely no-one uses it as a food additive, that should give you some considerable concern.
Aside from that, it's not water-soluable.

The Environmental Working Group (EWG) has a factsheet

Classified as expected to be toxic or harmful

Cameo* (a pigment/paint/colour authority) says this:

Hazards and Safety
Toxic. Inhalation or ingestion of manganese can cause a nervous system disorder.

For lists of approved food additives - see Wikipedia; E number

*Cameo - The Conservation and Art Materials Encyclopedia Online (CAMEO) is an electronic database that compiles, defines, and disseminates technical information on the distinct collection of terms, materials, and techniques used in the fields of art conservation and historic preservation.