again?

The question is substantially different

Yes, sentences change meaning in different contexts. We knew that already; the truth or falsity of that doesn’t correlate to the existence of paradoxes, though. Some languages (mostly constructed) are designed specifically to be completely unambiguous, although the humans involved can very-easily create ambiguity intentionally. I don’t see what that has to do with the liar’s paradox.

Last try: the Liar is due to SELF-REFERENCE. Human languages have billions of sentences that are not self-referntial: "This rose is red". There is no interest in showing that avoiding self-reference we can "solve" the Liar: we already know it. The issue of the Liar is simply that with a very limited amounts of "resources" (self-refernce included) we can manufcature so big a puzzle.

The assumption that sentences do not change their content across occasions of use, i.e., that they display no context-dependence, leads to the Liar paradox, in fully interpreted (formal) languages given Convention-T because then we cannot make a distinction between (1) and (2) and for example the predicate "is false" has in every context the same meaning. Notice that (1) and (2) can have a different unambiguous meaning in a different context

@MauroALLEGRANZA notice that (1) is still self-referential , we just made an assumption about the meaning of the predicate "is false" involved in (1) and by flawless logical reasoning we concluded that "is false" in (1) cannot have it's usual meaning it must have an unusual meaning in (1) by logical necessity.

Are you just asking whether sentences take meaning from context? Or are you just looking for an explanation of what makes the liar's paradox seem a paradox? Both have been answered elsewhere on this site.

The usual meaning of "is False" is "it is not True. If you have changed its meaning, what is the meaning of "is either true or false, not both"?

@MauroALLEGRANZA its usual meaning ;)

@MauroALLEGRANZA I have not changed the meaning of "is false" in (1) , I supposed that it has it's usual meaning and it cannot have it's usual meaning by logical necessity.

The definition of any word (if they actually have definitions at all) is part of its context. Your use of 'usual meaning' implies this. In conversation, most of us use "is false" to mean "there is something wrong with this" rather than "is not absolutely true in every detail". We may approach the other meaning when we discuss Aristotle's excluded middle. Are we discussing the excluded middle? That's context.

But see Donald Trump for a clear example where "true" and "false" have not their usual meaning.

@JonathanZ I supposed that

In that particular instance, Mauro’s got you. It’s not fake news if you can go to Truth Social and check for yourself. Richard Kirk also nailed it: literally every piece of human language is context-dependent.

Consider the sentence "My name is Joe". The truth value of this depends on who says it, so it's clearly context-dependent.

Even though this question is extremely similar to some earlier ones, and even though the OP seems to be pushing for a "personal philosophy", I vote to reopen this question. The last specific question makes it different enough from the earlier ones, imo. Similar ideas as the one that the OP is trying to figure out have also been proposed by several philosophers. For instance, Yehoshua Bar-Hillel and others suggest the "simple" solution of the Liar that truth is not a property of sentences but of propositions, and that the analogue "The proposition expressed by this sentence is false" is ...

(continued) ... either false (or neither true nor false) because its noun phrase doesn't denote any proposition (so the sentence does not express a proposition). There are arguments against this, but it's not an absurd point of view.