https://en.wiktionary.org/wiki/wedgie
"A situation where a person's underpants are stuck uncomfortably between their buttocks."
Collins: the state of having one's underpants or shorts caught between one's buttocks

It's not just a prank. 
I agree with you about sense 4, but I think both senses are actually just examples of sense 1. It's just that GG5's glosses are a bit odd.

@@ -12,2 +12,2 @@
-<gloss>intrusion</gloss>
-<gloss>thrust</gloss>
+<gloss>digging into (e.g. one's skin)</gloss>
+<gloss>cutting into</gloss>
@@ -28,5 +28 @@
-<gloss>something that digs into one's skin (e.g. a hairband on a wrist)</gloss>
-</sense>
-<sense>
-<pos>&n;</pos>
-<misc>&vulg;</misc>
+<misc>&col;</misc>

wedgie
an act of pulling up the material of someone's 
underwear tightly between their buttocks as a 
practical joke.

Google Images is all about sense 5 
(underwear/clothing stuck between the 
buttocks/vulva). I think it should be placed 
first, but probably in a more general form 
like in jitsuyo (with an "esp. of underwear" 
type of thing). I don't think "wedgie" is 
correct at all, it's not a prank, it's the 
underwear being pulled up into the buttocks 
(for whatever reason). I don't think sense 4 
is a separate sense from sense 5.

I don't have access to the original submission, but www images are fairly explicit.

https://twitter.com/jtzook/status/1351635697849942016

"evidently anything that digs into your skin can be 食い込み, so the author here (jm dict?) may have been a bit too... precise 
this time (src: native speaker sitting next to me)"

may be Jisho's issue I'm referring to, but still, there is one sense of the phrase missing from JMDict. thank you! JZ

@@ -24,0 +25,4 @@
+</sense>
+<sense>
+<pos>&n;</pos>
+<gloss>something that digs into one's skin (e.g. a hairband on a wrist)</gloss>