Austria funds a good deal of psychotherapy, through a mechanism that is easy to misread. The health insurer doesn't have therapists of its own. ÖGK holds no contracts with individual psychotherapists at all. Instead it contracts associations, which hold the fully funded places and allocate them. So finding a funded therapist in Vienna is really a matter of getting a place from an association.
In Vienna the two main associations are the Wiener Gesellschaft für psychotherapeutische Versorgung (WGPV) and the Verein für ambulante Psychotherapie (VAP), alongside several contracted institutes and outpatient clinics. You don't need a referral. You need to be insured, and you phone them. A funded place costs you nothing. The difficulty is that places are capped, so there aren't enough of them.
The other route is to see a therapist in private practice, pay them, and claim part of it back. ÖGK refunds €33.70 for a 60-minute individual session. BVAEB and SVS, the funds for public servants and the self-employed, refund about €50 for the same session, so which fund you belong to changes what you get back by roughly half as much again. A doctor has to confirm there is no physical cause before your second session, and the insurer has to approve continuing after the tenth.
The reason you are there has to be a diagnosable condition. ÖGK says plainly that it doesn't pay for counselling about school, family or work problems, which means a good deal of couples work and life counselling is paid for privately in full.
On It's Complicated there's no association to phone, no queue and no diagnosis required. You choose the therapist and arrange it with them directly, and if you want to work in English, or on something the insurer doesn't treat as an illness, it's the more predictable route.
Psychotherapeut:in is a protected title in Austria, and everyone holding it appears on a public register kept by the health ministry. Klinische:r Psycholog:in is protected separately, with its own register. Lebens- und Sozialberater:in, life and social counselling, is a trade licence rather than a health profession, and psychotherapy is explicitly excluded from what it permits. A Psychiater:in is a medical doctor who can prescribe.