Ok, I’ll edit this later but I tested 6 of the abilities with Sticky Web, Toxic Spikes, Spikes, and Stealth Rocks up (as well as some other things like Sand Stream to activate Cloud Nine and HP Fighting to activate Anticipation) NebbyY helped me with this, putting together the entry hazards team. Here is the replay. As you can see, the entry hazards acted before all of the entry abilities. Again, I’ll edit this once I test out the other abilities. Here is the team I used.
Also, as I said in the answer to that question you linked, Misty Surge activates after Toxic Spikes, so I’m also going to assume the same for Electric Surge, Psychic Surge, and Grassy Surge.
Hope this helps! :)