Fix several reported issues in String's documentation

[Mickeon]

Closes godotengine/godot-docs#8043
Closes godotengine/godot-docs#8044
Closes #86734
Mitigates godotengine/godot-docs#8190

This PR updates the String's class reference slightly.
It formats uppercase and lowercase in their respective String methods and removes a seemingly useless note in String.capitalize() and incorporates it with the example code, instead.
Finally, for StringName, it adds a note exclusive to C#, because all of the listed methods are not available there. This note is almost word-for-word taken from the bug report godotengine/godot-docs#8190 (@raulsntos)

Oh great heavens, news flash. Let's also add some examples for #86734, why not.

Could be easily cherrypicked for prior Godot 4.x versions

[Mickeon]

Sounds good. I changed and removed part of the StringName C# note. I would also say that the PR no longer fully addresses godotengine/godot-docs#8190 because it needs to be stated clearly in the C# differences page, too.

[raulsntos]

I think you could make the change to CLASSES_WITH_CSHARP_DIFFERENCES in this PR:

diff --git a/doc/tools/make_rst.py b/doc/tools/make_rst.py
index c3a21f3d7b..df3e928538 100755
--- a/doc/tools/make_rst.py
+++ b/doc/tools/make_rst.py
@@ -105,6 +105,7 @@ EDITOR_CLASSES: List[str] = [
 CLASSES_WITH_CSHARP_DIFFERENCES: List[str] = [
     "@GlobalScope",
     "String",
+    "StringName",
     "NodePath",
     "Signal",
     "Callable",

[Mickeon]

Oh that's neat, I did not realise part of it could have been done in the same repository. Done.

[raulsntos]

LGTM.

[Mickeon]

Addressed the above feedback with an additional note. I didn't want to add the explanation in the same line, to keep the short summary consistent to the other similar methods.

[akien-mga]

Thanks!

[YuriSizov]

Cherry-picked for 4.2.2.

[YuriSizov]

Cherry-picked for 4.1.4.