> 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. 

This is correct. You are already an Austrian resident whose rights derive from the EU freedom of movement, at least after you applied for the residence document. In fact the deadline to apply for a formal document related to Brexit is even later (but it is good to apply as soon as possible).

> However, they also mentioned that I can make an appointment for getting a visa in January

They might have mentioned that because if you need to leave Austria temporarily before your residency document is deliver, you could still get a visa so you can reenter Austria and/or have legal status in other Schengen countries. 

>  while had my form been delivered a couple of days earlier, I would not have needed a visa at all.

From 2021 your unstamped British passport alone without other documents may soon be insufficient to prove your legal status in the Schengen area nor does it give you permission to enter EU for purposes other than a simple visit. With the Covid regulations, it is particularly important as you might be denied boarding/entry to EU/Schengen without proof of residency (like a permit or visa).

-------

> You and your family may need to apply for a residence status to confirm that you were already resident in the EU country you live in before 31 December 2020. You will have until at least 30 June 2021 to do this.
>
> https://www.gov.uk/guidance/living-in-europe#uk-nationals-in-the-eu

>**UK nationals living in Austria before 1 January 2021**
>
>You will need to apply for a new ‘Article 50’ residence card to remain in Austria. You should apply in person through your local authorities. Check in advance if coronavirus restrictions are affecting office opening times or procedures.
>
>In Vienna, you will need to make an appointment at the MA35 (local immigration office) in Arndtstrasse.
>
>You must apply between 1 January 2021 and 31 December 2021. Read the Austrian government guidance on the residency registration process.
>
> https://www.gov.uk/guidance/living-in-austria#visas-and-residency

See also [Austrian government's guide for British citizens][1]. You will need to apply for an Article 50 card also.

Particularly
> Do you have a registration certificate, certificate of permanent residence, residence card, permanent residence card or a permanent residence permit (permanent residence - EU)? Then this is helpful for your application. However, your further right of residence is not dependent on these documents, which means that you can also apply for a residence title under "Article 50 TEU" without these documents.


  [1]: https://www.bundeskanzleramt.gv.at/en/topics/brexit/residency-and-access-to-the-labour-market.html