With the snapshot, containing the Brigadier Command-System, it is not (easily) possible, to teleport (non-player) entities relative anymore.

I am aware, that the old behavior of the tp command is non-existent anymore and that

tp @e ~ ~1 ~

teleporting all entities (including yourself) above yourself is correct, instead of teleporting every entity up relative to itself.

However, doing this with execute is not possible either in the snapshot:

execute as @e at @s run tp ~ ~1 ~

or

execute as @e at @s run tp @s ~ ~1 ~

Which is in my eyes the way to do it, will give an error message, that a relative teleport requires a player to run.

Therefore the only possible way of doing a relative teleport on something, that isn't a player currently, is by summoning a temporary entity and teleporting to that.

In my eyes, it is a bug, that a relative teleport requires a player as an executor.