we use by when something happens by a time in the future not until

Question

"It's too late to go shopping. The shops are open only until 5:30. they will be closed by now."

First: what is closed here? an adjective?

Meanwhile:

Taking the italic part into account, there has been obviously mentioned the fact that if something happens, then we use by. Nevertheless, in my original question, the following phrase is just a statement not an action, so why don't we use until?

"Closed" represents a state, not an action.

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EDITED:
My biggest and most important and specific question:

My specific question, now, is about the fact that considering the following explanations, and as being closed is just a statement not an action, why does my original sentence use by rather than until?

The followings are extracted from the book English Grammar in Use:

1 until
Something continues until a time in the future:

Fred will be away until Monday. (so he'll be back on Monday) I'll be working until 11.30. (so I'll stop working at 11.30)

2 by
Something happens by a time in the future:

Fred will be back by Monday. (= he'll be back not later than Monday)
I'll have finished my work by 11. 30. (I'll finish my work not later than 11. 30)

C. You can say 'by the time something happens'. Study these examples:

It's not worth going shopping now. By the time we get to the shops, they will be closed. (= the shops will close between now and the time we get there)

. . .

UNIT 119 By and until, By the time...

A. By (+ a time) ='not later than':

• I posted the letter today, so they should receive it by Monday. (= on or before Monday, not later than Monday)
• We'd better hurry. We have to be at home by 5 o'clock. (= at or before 5 o'clock, not later than 5 o'clock)
• Where's Sue? She should be here by now. (= now or before now - so she should have arrived already)

You cannot use until with this meaning:

• Tell me by Friday whether or not you can come to the party. (not 'Tell me until Friday')

Answer 1

It’s too late to go shopping. The shops are open only until 5:30. They will be closed by now.

Yes, closed here is employed as an adjective. You are correct in understanding it to designate a state rather than an event.

And it is true that the expression by TIME is used with events rather than states—as your source says, it says that something ‘happens’ (an event) rather than ‘continues’ (a state).

HOWEVER: The expression by TIME does not compel you to employ an ‘eventive’ predicate or forbid you to use a ‘stative’ predicate. In fact, the compulsion works in the opposite direction: when you use by TIME, you compel your hearer to understand the predicate in an eventive sense. With by TIME the hearer interprets a stative predicate as the result of a change of state: something happened before TIME to bring about the state you describe.

Here are examples of by TIME with three stative verbs, know, own, be:

By April he knew that the operation was a failure. ... implies that he did not know this earlier, but at some time before April he learned that the operation was a failure

By 1973 he owned 26 newspapers. ... implies that he did not own so many newspapers earlier, but at some time before 1973 he acquired 26 newspapers

By next week you will be in Toronto. ... implies that you are not in Toronto now, but at some time before next week you will go to Toronto

In the same way, The shops will be closed by now implies that earlier the shops were open, but at some time before now the shops were closed. Since it is explicitly stated that the shops are open until 5:30, we understand that this sentence must have been uttered at some time after 5:30.

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The word will may have caused you some confusion. This will does not designate some time in the future; it expresses a certain inference in the present. (Linguists call this ‘epistemic’ will.) Your last sentence may be paraphrased

It is certain that they are closed by now.