though I'm not actually sure if there are any significant differences between calling webdev serve and pub build_runner serve (which is what Dart Code has support for)?

webdev serve is the same as pub build_runner serve (however, we generally want to treat webdev as our entry-point for tooling).

we generally want to treat webdev as our entry-point for tooling

Is it stable enough that we'd be happy to ship integration with it? Currently we detect build_runner(?) in the pubspec to show the build_runner tasks, it wouldn't be difficult to also detect webdev and show them (presumably we'd want to hide the build_runner ones in that case?).

I'll land this as-is for now, but we can update it when the Dart plugin understands webdev.

Is it stable enough that we'd be happy to ship integration with it?

Yes, and more work is being put into it currently.

it wouldn't be difficult to also detect webdev and show them (presumably we'd want to hide the build_runner ones in that case?).

This sounds reasonable; generally I think we want to either only show webdev items, or at least prefer them. My understanding is that build_runner is more on the level of plumbing.

generally I think we want to either only show webdev items

Will webdev be in the pubspec for projects it's valid for, or can uses pub global activate it? (I need to know which projects it's valid to use for).

My understanding is that build_runner is more on the level of plumbing.

For non-web users (Flutter, CLI) is there some equiv to webdev run the codegen/start watching? (I figured they'd always use build_runner).

I think that pub global activate will be the most common way to run it - there may not be much indication in the pubspec that its in use.

For non-web users (Flutter, CLI) is there some equiv to webdev run the codegen/start watching?

I'm not certain here -

Ok, I've opened Dart-Code/Dart-Code#1412 about changing over - though we'll need to figure out how to identify which projects to use webdev for!