austria – Rights of UK citizens midway through residency application to EU

I am a UK citizen living in the EU, and am partway through applying for residency in Austria. That is, I have registered my apartment and submitted all the necessary documents (proof of address, identity, income etc) to the local government immigration office, along with various forms. This process ended up taking a lot longer than expected, partly due to Covid, but everything was approved and I was supposed to have received a form that I needed to sign and post back in order to get my residency certificate.

As of 31st December 2020, the form has not arrived. Since tomorrow marks the end of the Brexit transition period, I am not sure whether or not I will retain my EU rights (freedom of movement, access to EU social security and jobs market, indefinite leave to remain in the country, etc), since my application was only part-completed at this time.

I emailed the state office, asking if there was an electronic version of the form I could print out myself and send by special delivery to ensure it arrived before the Brexit deadline, since otherwise I would need a visa to remain. Their reply was that “it is not a problem, since (I) have already taken advantage of freedom of movement (by coming to Austria before the end of the transition period)”. This seems to imply that because I have been resident since the summer, it does not matter when the official residency certificate is granted. However, they also mentioned that I can make an appointment for getting a visa in January, while had my form been delivered a couple of days earlier, I would not have needed a visa at all.

I’m not sure if this is some kind of communication issue (my German is still extremely limited) but if anyone knows what the immigration status/EU rights are for UK citizens with half-completed residency applications at the end of the transition period, that would be very helpful to know.