I'm still having trouble grasping this. Let me try and restate what your solution is doing:

   ^
   (               # capture delimiter in pos 1
       ["']        # delim is single or double quote
   )
   ((?!.*\g1.).*)  # neg lookahead for delim
   \g1$            # finally, the delim
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Pick up the delimiter character from pos 1, if there is one (otherwise fail)

Capture this in $2:

-- As many characters as possible (could be none)

-- that are NOT followed by the delimiter character and another character (which is the case of an embedded delimiter, which should be a fail)

-- and are followed by zero or more characters.

Beyond this should be the delimiter, at the end of the string.

I'm confused by the '.*' that's the last part of capture group $2. Why is it needed at all? Hasn't the preceding already consumed the payload that I want? I guess I'm not understanding the precise role that the negative lookahead is playing. Is it simply saying what the string picked up by .* must look like? Is there any significance to (?!.*\g1.) appearing *before*, rather than after, .* ?