'Case' refers to whether a verb is nominative, accusative, or genitive.

Case (verb)

And 'case' also refers to the upper or lower case of the first letter of a noum in a sentence.

Case (noun)

So just to say 'case in the text' would be ambiguous.

It would better to stay with the word 'capitalization'.

If someone grading a paper of mine commented, "Please fix the casing in your text," I would never guess that they meant capitalization. Instead, I would guess that they were referring to the "case" of nouns that Nigel pointed out.

If you are talking to the general public, I'd say that "casing" is NOT a valid alternative to "capitalization." However, if your audience possesses knowledge of very specific, language-related terminology, you might be able to get away with "casing."

If you are looking for an alternative way to say "Capitalization," I'd suggest "orthography," but this can refer to both spelling and punctuation.

Notice that your Wiktionary definition for casing says "computing". That means that casing is a technical term in the field of computing. If you use it outside of that field, then people may not understand you.

If you said to me as a software developer, "Fix your casing", I might understand you to mean, "Fix your source code so that it follows house style guidelines for casing convention." A casing convention is, for example, UpperCamelCasing or lowerCamelCasing for particular identifier types.

I think the Wiktionary quote gives an important hint: computing. It's perfectly valid to use casing in this sense in the context of programming for example, as you can see on Stack Overflow:

• Keep casing when serializing dictionaries
• Change Casing in WCF Service Reference
• Why do 'Infinity', 'null', 'NaN' and 'undefined' have inconsistent casing?

And on other computing sites on the SE network:

• Fix File Path Casing
• Change character casing on deployment

You'll also find it used in terms like camelCasing, and PascalCasing.

Looking at the profiles of the users who asked the questions you linked, you'll find that they all have Stack Overflow accounts with some rep. In other words, it would not be unreasonable to assume that they are programmers. It seems to me that casing does not see much usage outside of computing, except where it is used by programmers (but this might change in the future).

"Grammatical casing" is very rarely used (and is perhaps not entirely idiomatic) to mean "grammatical case" (example). The term "[letter] case" (which is equivalent to casing in meaning) sees usage outside computing (particularly in typography) but is easily confused with "[grammatical] case". For this reason, your example may be confusing to some people.