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According to this wikipedia article, Constrained writing is a literary technique in which the writer is bound by some condition that forbids certain things or imposes a pattern. The same link also provides examples of constrained writing. I will mention a few for reference:

Ernest Vincent Wright's Gadsby (1939) is an English-language novel
consisting of 50,000 words, none of which contain the letter "e".

let me tell you (2008), a novel by the Welsh writer Paul Griffiths,
uses only the words allotted to Ophelia in Hamlet.

How do readers come to know about used and hidden constrained a work has used? Do authors openly promote or do marketing of the same? What is the proper way to notify readers from the work itself that it has used some constraint?

You do not.

Nowhere in Green Eggs and Ham does Dr. Seuss tell you that the whole thing is written using exactly 50 different words. It's an "Easter Egg" as @Alexander points out in a comment. It's for readers to notice, or learn about from others having noticed.

An Easter egg is fun because the reader has a moment of "oh cool, it really is only 50 different words, I haven't noticed it before" (to continue with the same example). Had Dr. Seuss informed the readers of the constraint, the effect would have been instead "author stroking ego with unnecessary BS".

Discovering that a verse is in fact an acrostic, or that the novel doesn't use a certain letter, or anything similar, is only fun when you discover it yourself, or when a friend shows you and then you go and check for yourself. It's not fun when the author tells you about it, and takes away from you the glee of the discovery. You wouldn't want game developers to publish a list of all Easter Eggs when they release a game, right? They wouldn't be Easter Eggs then. Same here.

Crucial to the Easter Egg effect is that the piece of literature must be thoroughly enjoyable without ever finding the Easter Egg. Green Eggs and Ham is fun regardless. The Easter Egg is a nice bonus, it's not the main thing your creation has to recommend itself.

First of all, I think that that kind of serious constraint is mostly a stunt. It can be interesting, once. Usually an introduction or blurb for that sort of work explains the constraint, and why the author adopted it. Sometiems, particularly with a milder constrant, the reader is just left to figure it out.

For example, "Uncleftish Beholding" (1989) by Poul Anderson begins:

For most of its being, mankind did not know what things are made of, but could only guess. With the growth of worldken, we began to learn, and today we have a beholding of stuff and work that watching bears out, both in the workstead and in daily life.

The underlying kinds of stuff are the firststuffs, which link
together in sundry ways to give rise to the rest. Formerly we
knew of ninety-two firststuffs, from waterstuff, the lightest and
barest, to ymirstuff, the heaviest. Now we have made more, such
as aegirstuff and helstuff.

This is in effect a popular science article written in an alternate English pruned of words with Latin and Greek roots, relying on words (and new compounds) with germanic roots instead. This is a significant constraint, but the first publication did not, if I am correct, explain it. Later re-printings did, in an author's note or introduction. See this Wikipedia article for more information.

For another example, i once wrote a couple of short pieces where we were presented with one character's thoughts, but not his words, and heard another character's words, but not his thoughts. Sort of a variant on the classic one-sided overheard telephone conversation. It worked, but was a bit clumsy at times, and would not have worked for more than a few pages.

So if you choose to engage in such constrained writing (and why not) I would suggest including an introduction in which you state the constraint. But there is no rule on the matter.