Recalling standard results in a master's thesis appendix for reader's convenience and/or self-containedness

My answer is very similar to the one I gave to the question I linked to in a comment: There is usually no reason not to include something in a thesis. Your thesis is a place for you to give a coherent account related to your work on a topic. There are (usually) no page restrictions, and it should serve as a reference document for future readers.

Many theses include a lot of review material, beyond just what might be contained in a literature survey. A thesis has to contain new material, of course, but it does not all need to be novel, and there can be a lot of merit in giving detailed explanations of known results, if the readers are not necessarily going to be familiar with them in detail.

If you're just going to repeat the statement of the theorem for the reader's convenience, then I would just include it in the text at the point where it is used. I wouldn't send the reader to the appendix, unless the statement is exceptionally long (say a page).

If you decide you want to include a proof of the theorem, then I would put the proof in the appendix (and repeat the statement of the theorem there as well). This is not too unusual in a master's thesis, if you feel it would be a good exercise for yourself to prove the theorem. But it should be your proof; don't just copy a textbook proof verbatim.

You are looking for a decision between two alternatives - to cite you:

1. just citing the name of the theorem when I use it in the main work without giving any reference, or
2. rewriting the theorem in the Appendix for the reader's convenience (with appropriate reference to a "basic" textbook).

I'd go with alternative number 3:

3. give the theorem, along with a reference that allows the interested reader to follow up - that is, something like "(Foobar, 2016, Theorem 3.14)".

It makes sense to give this information, especially for propositions that non-experts may not know immediately. Conversely, I don't see the point of rewriting a theorem and its proof in an appendix. If you are too literal in copying, you are close to plagiarizing (unless you clarify that you are copying something verbatim - but then, why do this?), and if you reformulate, you run the risk of introducing errors of your own. Better to rely on standard textbooks.

Yes, a thesis should be self-contained, but of course it never is, and if you use a result from a standard textbook, then this should be easily available to any interested reader.

Of course, if you need to refer to more obscure material, possibly in a foreign language, or if you need to discuss the referenced result in some way, perhaps to point out an error in a proof, then it makes sense to devote more space to it. In an appendix, if the discussed material is not really germane to your main topic.