That RNLI “stay calm and float, then start swimming” advert is rubbish. I’d stay calm, sink to the bottom and then start walking to shore!
You should float,
Muscle has a density of 1.06 g/cm3
Fat has a density of 0.9 g/cm3
Bone around 2.9 to 3.8 g/cm3 depending on sex, diet, age and exercise.
But on top of that you have about 6l (about 7-10% of your total volume) of air in your lungs which will keep you afloat. So if you lie back you will float with your head above water. You’ll also have air trapped in your clothes so taking a moment to adjust keeps it there before you have to start planning what you’re going to do next.
If you hit the water, panic, breath out and thrash all the air out of your clothes then you’ll probably sink (or get cold water shock).
If you breath out completely most people will sink (you don’t need to be that skinny to do it, sorry to dssapoint) even tubby funsters can have their body fat measured by weighing themselves underwater.