If I had used Muk & Alolan Muk GX's "Severe Poison" attack that places extra Poison damage counters and in the next turn use Koga's Trap, do they still place the extra Poison damage?
No, they don't. The new, normal Poison Special Condition replaces the old Severe Poison Special Condition.
Source: Unbroken Bonds FAQ (2019-04-19), TPCi Rules Team (2019-05-02)

Relevant cards

Note: All applicable cards may not be listed below.
SM10_177
SM10_177
SM10_196
SM10_196
SM10_197
SM10_197
SM10_211
SM10_211
SM10_220
SM10_220
SM10_61
SM10_61