https://jacobin.com/2021/05/new-zealand-labour-party-sociali...
If anything, left/right does not mean anything in the US due to the radically different Overton window. As a European, I would consider the Democrat party to be right-wing. If you want left-wing, you have to go as far as Sanders or AOC.
Ireland: 0 years
The Netherlands: 2 years (Kok - 2000-2002)
Belgium: 3 years (Di Rupo, 2011-2014)
France: 5 years (Hollande - 2012-2017)
Germany: 6 years (Schröder - 2000-2005, Scholz - 2021-now)
United Kingdom: 10 years (Blair - 2000-2007, Brown - 2007-2010)
Austria: 18 years (Fischer, 2004-2016, Buren - 2016-2017, Van der Bellen - 2017-now)
So yeah, with the exception of Austria and arguably perhaps the UK, western Europe is pretty right-wing. In general, Western Europe has been very heavily on the neoliberal train since the 90s, including a significant amount of privatization. The current state of healthcare is a direct result of this.
1.
You listed the Austrian presidents rather than Prime Ministers. Under normal circumstances, the Presidents dutys are mostly of representative nature. They don't need to come from the same party and are not elected at the same time.
2.
> left-wing parties have ruled for the past X years in ...
The Schüssel governments from 2000 to 2007 were composed exclusively of right-wing parties, every government since then was a coalition of both right- and left-wing parties.