I found the Hotel Mozart from the brochure requested from the Salzburg TI resource Perry mentions. Keep in mind that the Austrian Hotel "star" system categorizes hotels by features and/or services and not necessarily by the quality of those features/services.
Hospitality Europe, the hotels associations of Austria, Czech
Republic, Germany, Hungary, Netherlands, Sweden and Switzerland have
created the Hotelstars Union. In the meantime, the following countries
joined the star family: Estonia (2011), Latvia (2011), Lithuania
(2011), Luxembourg (2011), Malta (2012), Belgium (2013), Denmark
(2013), Greece (2013) and Liechtenstein (2015).
Their partnership is providing a harmonised hotel classification with
common criteria and procedures in the participating countries.
Explaination of the star system criteria:
For example, to be rated as a one star property:
100 % of the rooms with shower/WC or bath tub/WC
Daily room cleaning
100 % of the rooms with TV together with remote control
Table and chair
Soap or body wash at the wash basin
Publicly available telephone for guests
Beverage offer in the hotel