They do get waterlogged, water can flow through big dripleafs but they can definetly also be in a source block.
This is not a bug, it is about water flowing mechanics. There are other blocks in Bedrock that work this way too, such as lever, repeaters and end rods. If anything it is a parity problem for Java since their water logging is a lot less of a complete feature, having some blocks that work like this is actually very useful. Anyways like what was already said this is not a bug since the difference is from before 1.15, and yes, not all blocks block flowing water on Bedrock.
I agree, it's only possible with commands and it seem like it will allow some cool builds in Creative so I don't think it should be removed.
The same thing happens with levers, repeaters, comparators, string, and tripwire hooks and I think it is intentional. Although I haven't used it, having a block which water can flow through could probably be useful.
You could always use something like a sign but still, I guess I understand buttons, but water flowing over pressure plates would be useful
I now understand that it's this way because when the piston is extended there is airspace in the body too so it need to have water there to avoid an air pocket underwater when it is open but it is still weird for making redstone.
I think they have trouble opening them as well. Sometimes they don't seem to be able to get inside at night.
It's not a problem with the world, I've tested it in multiple brand new worlds.
This seems to be fixed in 1.2
I wasn't claiming it can't be fixed and would require changing mechanics or that it wasn't different than Java, just that it isn't nessecerilly a bug. As was said above parity differences from before 1.15 are not considered bugs and since Bedrock has many similar block to this it is not strange behavior for dripleaf to behave in this manner too.