What happened in the late 2000s then with Liverpool, Arsenal, Chelsea and United getting to several CL finals and semifinals?
Did they do it without ‘modern tactics’? Were they worse than they are now?
Not necessarily worse but not better either. I consider City a better team than any of those were in their respective primes. However, Liverpool is slightly worse than United in 2008 IMO. Yet I I think that this "generation" of EPL top clubs will eventually surpass them. Believe Chelsea will probably reach City levels at some point in the future while Liverpool may have already peaked.
Besides that, I think that the English dominance you are talking about occurred when the game wasn't very tactical whatsoever. As soon as the game became more tactical again their kick'n'rush approach was toothless both against possession-oriented as well as pressing and transition teams. 2008 with Spain winning the EC and Guardiola taking over Barca was a turning point. Even SAFs United was clearly inferior to Barca 2009-2015, Real 2014-2017 and Bayern 2013-2016. I think City is a lot closer to these teams and probably even on their level if you take out Barcelona 2009-2011.