The question is surprisingly easy to answer: Austrian is a language of its own – a standardized written language and one of several standard varieties of the German language. In many text programs such as Word, you can select Austrian as your document language. It also has it’s own IETF language tag: de-AT.
German as a whole is a so-called pluricentric language with several standard varieties. Thus, Swiss Standard (or High) German (not to be confused with Schwitzerdütsch) differs lexically and grammatically from both the Federal German variety codified for Germany and from Austrian Standard (or High) German. Likewise, Austrian Standard German shows differences to the other two.
For example, in written Swiss High German, the letter ß does not exist, and is replaced by ss. There are also numerous differences in written language in Austrian High German - including in the areas of word formation, conjugation, grammatical gender, spelling... These are taught in Austrian schools as correct written language .
There are also independent high-level language words that only appear in one of the three standard varieties.
Independent high-level Swiss words are called Helvetisms (parkieren vs. [ein]parken, Velo vs. Fahrrad), Austrian words Austriacisms (Trafik vs. Tabakladen, Erlagschein vs. Zahlschein) and federal German words Teutonisms (Grundschule vs. Volksschule [AT], Primarschule [CH], bohnern vs. wachsen [AT], blochen [CH]). There are of course many differences in the kitchen language (lamb's lettuce – D: Feldsalat, Ö: Vogerlsalat, CH: Nüsslisalat).
The differences in the standard varieties are therefore roughly equivalent to the differences in other multivariate languages such as English (American English, British English) or French (French in France and Canada, among others), Spanish, Portuguese…
As for the question of the dialect, Austrian isn’t one. Rather, there are a large number of dialects spoken in Austria, some of which even belong to different dialect groups (Alemannic, Central Bavarian, South Bavarian) and differ greatly from one another.
At best, there is an all-Austrian tonal coloration, which, to put it simply, may sound a little softer than German German, especially with regard to the pronunciation of consonants. But that is independent of the codified differences in written and spoken high-level language.
The Austrian language is a recognized official language in Austria, South Tyrol and in all EU bodies. It is also a recognized minority or ethnic group language in Italy, Hungary and Slovakia.
(Swiss German is also the standard language in Liechtenstein.)
In fact, the interpreters and translators of the EU had to be retrained for the German language when Austria joined the Union. Not least because there are clear differences in Austrian official German opposite federal German expressions (Bürgermeister = Oberbürgermeister, Klubobmann = Fraktionsvorsitzender, Angelobung = Vereidigung, in Evidenz halten = vormerken).
So, should Switzerland (or Liechtenstein) ever join the EU, further follow-up training would probably be necessary.