Sea Ray

If the tanks don't leak when full, then the leak must be above the full level, such as in the supply hoses and fittings, the vent hoses and fittings or in the discharge hoses and fittings. Or, the leak has "sealed" itself.

The loud burp is the clue. It sounds like filling the tanks trapped an air bubble, that then became pressurized as the filling continued, until sufficient pressure was created from increasing the level above the air for that pressure to find a path, burping air and water.

It may be that opening is partially / fully sealed, now that the bubble is gone.

Every time I fill my water tank I stop when water spits out the vent near the fill. IMO this ensures that a dry bilge means no leak.

Why not overfill your system, up to the maximum level that it will hold, to see if water leaks?

If dry under this test, then either the prior leak is above this level, or pressure was required to force out the water / air burp.

Was the tank initially empty during the problem, perhaps trapping air down low, that then got "super" pressurized by 50 gallons of water above? When I fill my empty water tank I keep the pump powered and a tap open until normal flow is established to avoid trapping air down low.

If this low level / highly pressurized bubble was the possible problem, then could this be recreated, empty tank refilled, but this time visually observing that low plumbing while wearing eye protection? Also making a video would be handy if something happens because I frequently get bored and an event like this could be interesting.

It may be required to carefully apply a low pressure to the tank, but that is super scary because of the possible problems that would result.