If your mother does not have permanent residency in Austria and she has been away for more than 6 months in a 12 months period, she will have lost her A50 residency rights (no longer resident). You can still apply under the Family re-unification rules BUT she needs to be Financially dependent on you (there is no health dependency, unless it’s discretionary) AND that needed to have been done within 3 months of entry. More details here: https://www.britishinaustria.net/faq/which-family-members-can-and-cannot-join-me-in-austria/
https://www.bundeskanzleramt.gv.at/en/topics/brexit/residency-and-access-to-the-labour-market.html
If that fails another option is Settlement Permit Gainful Employment Excepted but that has strict quotas and runs out quickly – https://www.britishinaustria.net/the-guide/residence/residence-permits-with-quotas/
PS: As an aside having a Hauptwohnsitz Meldezettel without any other residency paperwork does not necessarily mean someone is legally resident.
