If a player has effects, he/she should see them in the inventory and (optionally) in the right upper corner. After teleporting in other dimension with "/execute in <dimension> run tp <arguments>", there are no effects to see in the inventory (right upper corner). Although, the effects are still there. This can be proven with "/data get entity @s ActiveEffects" and by seeing the effect particles around the player. New effects (applying after /tp) work fine as well as clearing and applying the old ones.

What I expect:
See active effects in my inventory.

What happens:
I see no active effects in my inventory.

How to reproduce:
1) Join any world or server (where you are opped);
2) Apply any effect(s) to yourself with vanilla potions or "/effect give" command (mind the duration, as it should be longer, than the time you need to tp);
3) Teleport to any other dimension with "/execute in" command. If you are in overworld, then try "/execute in the_nether run tp ~ ~ ~"