I've looked at the code of TextCases a bit but can't say 100% sure what it does for the type "EmailAddress", however I do see that some types simply get routed to Interpreter:

Interpreter[type][strings]

If you try this:

Interpreter["EmailAddress"]["Lab_Wolfram_Interest_Group <Lab_Wolfram_Interest_Group@groups.wolfram.com>"]
"Lab_Wolfram_Interest_Group@groups.wolfram.com"

it does work.

You're right. But the addresses have already been evaluated (otherwise I wouldn't have received them) But what about if I force a wordcharacter first. Gives the same result but resolves your point.

f[x_] := StringCases[x, 
  WordCharacter ~~ (WordCharacter | "_" | "%" | "+" | "-" | ".") .. ~~
    Verbatim["@"] ~~ (WordCharacter | "." | "-") .. ~~ Verbatim["."] ~~
    Repeated[LetterCharacter, {2, 4}], Overlaps -> False]

This is a strange but annoying problem! I noticed you can do a stack trace. Is this the pattern used to find mail addresses?

So when I even use the standard StringCases I run into the same max recursion problem. I would think this must be a bug..?

str = "Lab_Wolfram_Interest_Group <Lab_Wolfram_Interest_Group@groups.wolfram.com>";
StringCases[str, ((WordCharacter | "_" | "%" | "+" | "-") ..~~Repeated[Verbatim["."], {0, 1}]) ..~~Verbatim["@"] ~~WordCharacter | "." | "-") .. ~~ Verbatim["."] ~~Repeated[LetterCharacter, {2, 4}], Overlaps -> False]

Would splitting the string be acceptable?

Flatten[TextCases[#, "EmailAddress"] & /@ StringSplit["Lab_Wolfram_Interest_Group <Lab_Wolfram_Interest_Group@groups.wolfram.com>"], 1]

I guess, there should be no recursion problem for any regular expression without function-calls in them...

Well, I don't know these things by heart, but you can do:

Needs["GeneralUtilities`"]
PrintDefinitions@NaturalLanguageProcessing`TextPosition`PackagePrivate`iTextPosition

to see the internals of TextPosition and click on the various links you will see in that document and go deeper in to the code and so on...

It seem to me the pattern used is "wrong" When I change it to

f[x_] := StringCases[x, (WordCharacter | "_" | "%" | "+" | "-" | ".") .. ~~Verbatim["@"] ~~ (WordCharacter | "." | "-") .. ~~ Verbatim["."] ~~Repeated[LetterCharacter, {2, 4}], Overlaps -> False]

it seems to work like a charm.

And after some deep digging, you get the string pattern:

NaturalLanguageProcessing`$TextPatternTable["EmailAddress"]
StringPosition[str, %]

How that is converted to regular expressions I'm not sure, I'll leave that puzzle to other people:

NaturalLanguageProcessing`$TextPatternTable["EmailAddress"]
StringPattern`PatternConvert[%]

{(?ms)(?:(?:[[:alnum:]\x{f6b2}-\x{f6b5}\x{f6b7}\x{f6b9}-\x{f6bc}\x{f6be}-\x{f6bf}\x{f6c1}-\x{f700}\x{f730}-\x{f731}\x{f770}\x{f772}-\x{f773}\x{f776}\x{f779}-\x{f77a}\x{f77d}-\x{f780}\x{f782}-\x{f78b}\x{f78d}-\x{f790}\x{f793}-\x{f79a}\x{f79c}-\x{f7a2}\x{f7a4}-\x{f7bd}\x{f800}-\x{f844}\x{f846}-\x{f84c}\x{f854}-\x{f86c}\x{f874}-\x{f875}\x{f878}-\x{f879}\x{f87d}-\x{f886}\x{f88a}_%+\-])+\.{0,1})+@(?:[[:alnum:]\x{f6b2}-\x{f6b5}\x{f6b7}\x{f6b9}-\x{f6bc}\x{f6be}-\x{f6bf}\x{f6c1}-\x{f700}\x{f730}-\x{f731}\x{f770}\x{f772}-\x{f773}\x{f776}\x{f779}-\x{f77a}\x{f77d}-\x{f780}\x{f782}-\x{f78b}\x{f78d}-\x{f790}\x{f793}-\x{f79a}\x{f79c}-\x{f7a2}\x{f7a4}-\x{f7bd}\x{f800}-\x{f844}\x{f846}-\x{f84c}\x{f854}-\x{f86c}\x{f874}-\x{f875}\x{f878}-\x{f879}\x{f87d}-\x{f886}\x{f88a}.\-])+\.(?:[[:alpha:]\x{f6b2}-\x{f6b5}\x{f6b7}\x{f6b9}-\x{f6bc}\x{f6be}-\x{f6bf}\x{f6c1}-\x{f700}\x{f730}-\x{f731}\x{f770}\x{f772}-\x{f773}\x{f776}\x{f779}-\x{f77a}\x{f77d}-\x{f780}\x{f782}-\x{f78b}\x{f78d}-\x{f790}\x{f793}-\x{f79a}\x{f79c}-\x{f7a2}\x{f7a4}-\x{f7bd}\x{f800}-\x{f844}\x{f846}-\x{f84c}\x{f854}-\x{f86c}\x{f874}-\x{f875}\x{f878}-\x{f879}\x{f87d}-\x{f886}\x{f88a}]){2,4},{},{},Hold[None]}