Minecraft Pocket Edition was renamed to "Bedrock Edition" along with many other editions in the multi-platform merger. The "Bedrock Codebase" project is the one you are looking for, with project key MCPE.
Per the youtube link's comments the user is using optifine. Is this a vanilla install of minecraft?
added print screens This is what was built on the multiplayer server.
I came across the same issue, I thought it might be to do with the fact that I had joined a paper server, so I tried it again on another regular server and the same inconsistent biomes appeared, I don't know really what's causing it but as violine1101 pointed out, the leaves don't change even though the biomes on F3 do, I can only speculate but it's possible that the client is viewing these 3 dimensional biome borders while the server actually still sees the regular 2D borders that you would see on a single player world, I have only tried observing this issue in version 1.16.4, I have been looking around for answers for about an hour and have found nothing helpful, so this is all I have come up with. I believe someone mensioned in a similar thread that the biomes in the nether changed depending on the Y level, if you go to the nether in a single player world using a mod to visualise biome borders, the same inconsistent borders are visible and while they roughly outline the different biomes and how they are seperated, they are still blocky like the ones you get on the server, perhaps it is a bug confusing biome mechanics with the ones in the nether? I don't really know what is causing these problems but I would really like this to be fixed because some mob farms depend on specific biomes to be efficient and right now it is getting difficult to build them on my server.