Unless I'm mistaken (might well be, not my area of expertise) for modular approval (i.e., for an approval that carries over to another product that incorporates the module) the module needs to be shielded:
"1. The modular transmitter must have its own RF shielding. This is intended to ensure
that the module does not have to rely upon the shielding provided by the device into which
it is installed in order for all modular transmitter emissions to comply with Part 15 limits.
It is also intended to prevent coupling between the RF circuitry of the module and any
wires or circuits in the device into which the module is installed. Such coupling may
result in non-compliant operation."
https://transition.fcc.gov/Bureaus/Engineering_Technology/Public_Notices/2000/da001407.txtWhich might explain the delays... The FCC ID they got is specifically not for modular approval though: "Modular Type: Does not apply", so perhaps they just realised they couldn't get modular approval for the module as designed?
So let's hope nobody tries to integrate the module into another product...