As a both a Bedrock and Java player, I can confirm that the music does continue to play outside the water in both versions. The problem is that in bedrock edition, the aquatic music will play whenever you go underwater for more than a second. This means you get aquatic music when going up bubble elevators, falling in a lake or briefly swimming underwater. The aquatic music is good music, but there are only three tracks that play whenever you go underwater for even a few seconds. Java edition waits until you are in the water for a fair amount of time to play the music, and it doesn't get rid of normal overworld music when you enter the water.
Timothy Ziemann
As a both a Bedrock and Java player, I can confirm that the music does continue to play outside the water in both versions. The problem is that in bedrock edition, the aquatic music will play whenever you go underwater for more than a second. This means you get aquatic music when going up bubble elevators, falling in a lake or briefly swimming underwater. The aquatic music is good music, but there are only three tracks that play whenever you go underwater for even a few seconds. Java edition waits until you are in the water for a fair amount of time to play the music, and it doesn't get rid of normal overworld music when you enter the water.