Wonder how *fast* the water comes in in situations like this? i.e. would
concrete floors and a drainage channel around the perimeter, leading to a
sump/pump do the job - or would the pump just get overwhelmed? (There's
the issue of where to pump *to* of course!)

Everything from water gently lapping up at your house and rising
imperceptibly slowly, to mudslides and tidal waves.

Sewers overflowing back into properties is a particular danger (in
emergency use sandbags in the loo), so automatic valves or "sea
toilets" may be necessary.