Versions Tested: Minecraft 1.18.2, Stylish Effects 3.1.0 & Tinkers' Construct 3.5.0.17 running on Forge 40.1.31.
Noticed in a modpack, then popped a clean environment in to test, since the pack had a couple hundred mods, wanted to check for interference first.
Same behavior with just Stylish Effects and Tinkers' Construct.

The Issue:
The inventory status effects overlay covers the pop-outs for Tinkers' Construct crafting stations.
Namely, the Tinker Station, which has a tool selection on the left, and then information about the tool being created, based on the components inserted on the right; thus being blocked no matter which side you choose for the Stylish Effects Overlay to try and mitigate.
The Part builder suffers to a lessor degree, since it only has the information pop-out on the right side, so can be mitigated by putting your overlay on the left.
Depending on which style of view being used in your mod, and/or how many effects active (even in compact view, 4 or more is enough to render almost unusable if on the left, and covers valuable information on the right.

Your overlay automatically disappears so as to not interfere with the Curios mod pop-out when it is present, and when the Minecraft inventory recipes pop-out is present, so a similar disappearance seems to be the desired behavior in this case.
In those cases, it is a button being pressed causing the pop-out to be there, whereas in these cases, it is automatic when interacting with particular crafting stations.

So, I found your debug mode, in a very round-a-bout way.
My bad, I haven't played since Forge was an upstart really, so the format used by your blacklist was confusing.
I actually found the class of the specific pop-ups quick, but could not figure out how that related to how Curios was formatted on the blacklist (installed Curios in test to find its GUI class).
Then I went through the changes you made on Dec 7th, to try and figure out what you did to fix Curios, and I felt stupid, and activated the debug mode :P

Anyways, I have it working on my end, without having to shut it off for all other inventories, or even all Tinkers' Construct blocks (they don't all have pop-out information and buttons).

The relevant ones are:
tconstruct:part_builder
tconstruct:tinker_station
tconstruct:smeltery

Though they are only named for their first case used in, they are reused for blocks afterwards that fit in the same category, but upgraded.
There may be other stations, with differing ones, I tested as many as I could find in JEI, and watched some tutorials on new versions of Tinkers' to test late game stations; but it has been a long time since I played the mod, and Minecraft in general, so a bit rusty, just getting back into it.

Hope that helps, It is a very popular mod, so I think those should go on your default blacklist whenever you patch next.
Thanks for the work, it is a very nice HUD for effects.

Thank you so much!
I was about to tell you of the debug feature, nice you found it already.
I‘lol definitely include these by default in the 1.19 port.

Included in v4.0.0 for Minecraft 1.19. Thanks again!