Summary:
Player data on a singleplayer world isn't used when that world is moved to/used with BDS.

Steps to reproduce:

1. Create a new local world, give yourself a bunch of items and tame a pet
2. Save and close the world
3. Upload the world to a BDS install and start the server
4. Join the server while still logged into the same account
5. Note you enter as a new player, items and levels are gone, pets are no longer yours etc.

You can move the world back to singleplayer and progress while the world was on BDS will be lost but items etc from before the move will be back.

What I expected to happen:
My player data should be linked to my account, allowing me to move it between BDS and Singleplayer without losing progress

What actually happened:
Player data is stored differently for local and network players causing inconsistencies when moving between BDS and Singleplayer.

Some more detail (all educated assumption):
At the moment when playing a world in singleplayer, your data is stored under a local_player entry (with no link to your xbox account). When that same world is moved onto a BDS and you connect you instead get a new player_server_guid entry. Because your progress is stored under local_player its not applied to the player.

Realms is able to get around this by (I believe) "copying" the player data of the local_player to the owners player_server_guid account.

BDS isn't linked to an "owner" in the same way realms are so the same process may not be possible.