Just to clarify, the 3rd primary vaccine (for the immunocompromised) and the 3rd booster injection (for those not in the immunocompromised/immunosurpressed group) are actually the same vaccine but used differently. This is because Pfizer is the currently available vaccine for most groups (it is also a mRNA vaccine which is recommended for the immunocompromised). The Moderna vaccine, not as far as I know in general use among the older population, is also a mRNA vaccine but it is normally given at too a low a dose to be effective as a booster for older groups. If Moderna is to be used as a 3 primary vaccine, then a double dose will be needed.
However, those having had the 3rd primary vaccine will be called for their (first) booster in 6 months.
The charity, Blood Cancer UK is the main source of my information. I 'follow' them on Facebook. A recent webinar of experts, who discussed the vaccination program and results of trials, started by focussing on the the roll out of the 3rd primary vaccine and I think that no-one watching would be in any doubt that there had been many problems. However, the experts on the webinar were not based in Scotland and they could only comment about the roll-out in England.
Although I have had my 3rd primary dose, I spent 4 weeks trying to find out how to get it. I ended up in a circular maze, specialist-GP-119-GP and only managed by applying through the PALS (Patient Liaison Group) after which I had a letter with an appointment.