That's right, Manual exposure is manual, it can only use whatever settings you set. Exposure compensation cannot change those settings you set manually, so it cannot change the Manual exposure.
Compensation does change what the meter shows, but Manual uses your manual settings and does not use the meter. Manual is manual. But you do have the option to choose the Manual settings according to the meter (settings to zero the meter). If done that way, it would seem to be metered exposure then.
An exception would be if you also set Auto ISO. Auto ISO makes Manual exposure become automatic (over the relatively small range of ISO). It still cannot change the manual aperture or shutter speed, but Auto ISO can adjust ISO to possibly make those settings be correct (over the range of that adjusted ISO). And then Exposure Compensation would change the target goal for the Auto ISO to seek.