Most people think that Google agenda could conflict with Microsoft agendas. I have read a LOT of chromium issues. I can tell you that the higher management at Google does not dictate chromium changes as they are too technical for them. The truth is, except for maybe a few exceptions, chromium evolve through the decisions of engineers that want to create the best possible product. They are not different to Firefox or edge engineers. Thus they should collaborate pretty well and a Google and Microsoft team should not have more "conflicts" than between two Google internal teams. As you said for the exceptions, Microsoft can maintain a fork, it's still order of magnitude more economic and smart than to constantly duplicate work in a redundant browser (firefox)
You can see a list of their merged pull requests here: https://chromium-review.googlesource.com/q/author:*.microsof...
BTW I really wonder when Apple will switch back to chromium.