Bathtub
An overflow and a pipe leak leave different stories. Keep them straight.
A filled tub that ran over is a one-time event. A waste shoe or supply line can look the same downstairs if nobody writes down what happened in the room above.
Ask what the tub was doing.
Was someone bathing? Did a child leave a tap on? Or did water appear with no one using the tub? That answer changes the investigation.
Overflow plates and waste shoes.
Water at the overflow is not the same as water at the drain shoe in the ceiling. Do not replace both on a guess.
One event versus a repeating drip.
A single overflow can still wet insulation. A repeating drip after the tub is idle is a different problem and should not be closed as ‘they overflowed it’ without evidence.
Questions people ask
Should I drain the tub immediately?
If it is still full and overflowing, yes, if you can do it without making the floor worse. Then stop using it until the downstairs ceiling is stable.
Does an overflow need leak detection?
Sometimes the overflow is obvious. If the downstairs damage does not match the story, investigate.