Austria will allow you to visit your partner as long as you can prove your relationship. The preferred documents are 1) a copy of your partner's passport, and 2) a copy of their residential papers confirming their residence in Austria. Pictures, letters, and other forms of proof are recommended to carry with you but may not necessarily be required.
A Pre-Travel clearance form is mandatory to fill out online, however, sometimes the form will not let you proceed if you're not an EU citizen. In this case, contact your local Austrian embassy and they will email you a pdf file to print out and fill out by hand and take with you to the airport.
A vaccinated card will get you in without any further restrictions. If no vaccination card, then you must present a negative PCR test dated no earlier than 72 hours from entry, or an antigen test no earlier than 48 hours from entry, PLUS a 10 day quarantine. The quarantine can be reduced if you were to obtain a negative test on your fifth day.