You are right that Google is aggressively pushing the web forward, but it's debatable whether it's a good thing; if you look at recent initiatives like FLoC, Web Packaging and Manifest v3.
Depends on the individual feature/standard. I'd say the vast majority of their work is not controversial or extremely beneficial to just Google, minus a minority of exceptions like the ones you mentioned.
What people forget is that IE was also very actively pushing the web tech forward (albeit not via standards), before the stagnation that was IE6.
IE pushed the web forward initially. It was only after it won that it stagnated. As a developer, this is my biggest fear for Chromium.
I honestly don't fear that. Times are different.
Google wants the web to succeed, whereas Microsoft saw it as a threat. In addition, in the case of stagnation it would be relatively easy for a Chromium clone to fill the gap.
Google wants Web == ChromeOS, it is their Windows, naturally they want it to succeed.
Android and Fuchsia are also ways to achieve it.
Chromium lacks lots of relevant features that most users actually want from Chrome.
The IE comparison in dominance would be accurate, but it's worthwhile to point out that Google aggressively pushes web tech forward, whilst IE largely stagnated it. I think that's a meaningful difference, at least to developers.
And it's not just a passing note either. Firefox' once strong position was made possible by the gap left behind by IE. There is no gap now. The dominant party is speeding ahead.
Edge is an interesting case, as it shows the vast power of Google. Edge's market share is an embarrassing 3.4% in total, and on mobile about zero.
This shows that even with a desktop monopoly, they can't push it effectively. Supposedly, desktop users still keep using Chrome. Why wouldn't they? Edge is Chromium. Further, Microsoft does not have a single mass consumer service (like gmail, youtube, etc) to push it either. On mobile, Edge has no meaningful presence, and if mobile is some 70% of traffic these days, one can only conclude that all powerful Microsoft is completely unable to push a browser.
If they can't, how can Mozilla?