However,
if you can't pull it back out maybe just drill a hole , put a small DRIFT into the hole and PUSH.....or tap gently against a soft wood block...endgrain of wood is best.
Air is a gas and is compressible- "compressed" air is denser and floats "lower" and thereby has less buoyancy. If the float originally had two domed convex surfaces and you have popped them inward,to "concave" you have changed the volume, you have compressed the air, you have reduced the buoyancy.
.....failing other tries,, you could add buoyancy with a light glue-on cap..epoxy should be ok but the addition must float the glue too.
I would consider de-soldering,correcting the "dish?",and resoldering. The rest of the bits could also fall apart unless you are careful and apply heat locally. This would be true resoldering over the hole above too so be careful. Heat sinks can help. I've used pairs of vice grips and forceps as immediate emergency heatsinks. I've resoldered old floats from outboards but they weren't dual like these and if the joiner is soldered too, it makes it tricky.
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