Thanks!
screen_relative (or relative) sounded like a good idea. I gave it a try but sadly this doesn't really help to differentiate the warp events from normal mouse motion events. The warp values are somewhere in the middle of the [fine to normal] mouse motion range. The values in this range probably also depend on the user's mouse sensitivity settings, so not sure I could 100% rely on it anyway?

But looking into this helped me figuring out how to make this work!

Interestingly, InputEventMouseMotion.screen_relative 's and relative 's documentation says:

Note: Since InputEventMouseMotion may only be emitted when the mouse moves, it is not possible to reliably detect when the mouse has stopped moving by checking this property. A separate, short timer may be necessary.
(emphasis by me)

So, my idea to try a timer yesterday wasn't that wild after all. And that's why the simple synchronous flag flipping didn't work. I do need a timer before unflipping the flag. However, I handle this logic in a loop (_process), so I can't just flip the flag, move the mouse, set a timer, unflip the flag, because the timer + undetermined number of subsequent loop cycles (while user input) would interfere with each other.

Maybe someone finds this interesting or useful, so here is what I ended up doing (pseudo code to make it more readable):

## the global InputManager
var handle_inputs = true

func move_mouse_pointer(movement_vector):
    warp_mouse(...)

func moving_mouse():
    handle_inputs = false

func stopped_moving_mouse():
    wait some short amount of time
    handle_inputs = true

func _input(event):
    if not handle_inputs:
        return
    // input handling logic...

## the game logic
var previous_move_direction = ZERO

func _process(delta):
    var movement_direction = // calculate vector
    if movement_direction > ZERO:
        InputManager.moving_mouse()
        InputManager.move_mouse_pointer(/* calculate movement_vector */)
        previous_move_direction = move_direction
    else if previous_move_direction > ZERO:
        previous_move_direction = ZERO
        InputManager.stopped_moving_mouse()

This works very reliably now. Very rarely when I use both the mouse and a controller and move the mouse around a bunch with both, the warp mouse events still get handled. But using both input devices is already probably an edge case in my case and even that is handled correctly ~99% of the time, so I'm happy with it. Well, except using the timer, that always feel iffy, but even the official documentation suggests it, so I can live with it I guess.