The C2 is surely a suspended chord.

a suspension is a note held over from a previous harmony. For example, to get to F you may go Bb (F, Bb, D,) to C sus 2 (G, D, E,) to C (G, C, E) to F (A, C, F). Thus the D note is suspended from the Bb chord to the C Sus 2.

With the suspended fourth there is almost the same thing: Bb (Bb, D, F), to C7 Sus 4 (G, Bb, C, F) to C7 (G, Bb, C, E) to F (A, C, F). Here there is a strong pull from the F to the E, and then a strong pull (actually the strongest musical pull) from leading note to tonic (E to F) and from the minor seventh of the dominant 7th chord to the mediant of the tonic (Bb to A).