When I tried to teleport to any entity to any entity using this:

/execute as <entity> at @s at @n[distance=0.01..] run tp @s ~ ~ ~

The entity executing the command or I won't get teleported.

It would work using this:

/execute as <entity> at @s run tp @n[distance=0.01..]

but there's still the problem when using similar commands to:

/execute as <tamable entity> at @s on owner run tp ~ ~ ~ 

because this is currently impossible due to the bug.