[Flyout System] Resizing the viewport to switch layout mode mode freezes the whole tab

[tsullivan]

Reported by @tkajtoch

Describe the bug

In Kibana PRs that utilize the EUI Flyout System, we see functional test failures with WebDriverError: tab crashed. There has been indication that resizing the window crashes the app.

Impact and severity

Severe: app crash

Environment and versions

Minimum reproducible sandbox

To Reproduce

From @tkajtoch investigation:

It seems like making viewport width to switch to side-by-side flyout mode freezes the whole tab and pausing execution crashes it
we've got an infinite loop and a memory leak somewhere - the number of event listeners goes up way high and memory usage keeps increasing (GC tries to clean it but it fails)

Expected behavior

Screenshots (Optional)

Additional context (Optional)

EUI release blocker