Words don't have any meaning anymore if react (and the HTML DOM) is considered anything close to "immediate mode".

For starters the DOM is a declarative thing - immediate mode means that you have a function called for each frame with imperative function calls written by the user of the immediate mode GUI toolkit for rendering each element of the GUI every time (unlike retained mode where a framework hides that behind some object model). It's not really possible to be more opposite to a declarative approach.

Flutter on the web uses the DOM?

I seem to recall discussing here on HN with people from the Flutter team how they didn't use the DOM on purpose.

Flutter isn't built on top of the DOM. And anyway that's not why they're not immediate mode. Take a look at some egui code and you'll see huge differences, e.g. in how button clicks are handled, when code runs, etc.