The `waitForClick` helper function is functionality-wise mostly a
reduced copy of the more generic `waitForEvent` helper function that
we use for other integration tests, so we can safely replace it to
reduce the amount of code.
Moreover, the `waitForClick` code is prone to intermittent failures
given recent assertion failures we have seen on the bots (one of them
is linked in #18396) while `waitForEvent` has recently been fixed to
avoid intermittent failures, so usiong it should also get rid of the
flakiness for these integration tests.
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