The issue of the paradox, its nature and extent was brought up in "The Liar Paradox - an explanation of the paradox from 400 BCE" (Jeffrey Kaplan, YouTube, 2023-03-15), currently linked here:
(in which he cracked a joke about using the term 'Fribbles' instead of 'Tribbles' to avoid CBS suits - a sort of inside joke.)
In one of the comments, it was noted that in the book Thief of Time by Terry Pratchett, the auditors of the universe, beings of pure order and logic, eventually overcame this paradox by classifying three types of sentences: True, False, or Bloody Nonsense.
In reply to that comment, below, the matters relating to both this - and to your question - were and are decisively resolved. This was the reply:
And in that universe, a civilization of cyborgs riding in spaceships shaped like Platonic polyhedra came along. They announced their arrival - "We are the Borg". The logicians replied "You can't say that. CBS will sue you." They responded "CBS/Paramount is irrelevant." The logicians replied "I beg to differ. They are quite relevant." The Borg responded "Their stock has been crashed from 97.35 in March 2021 to 20.00 in March 2023...". The logicians tried to interrupt "That was just market mechanics", but the Borg interrupted the interruption "We pumped and dumped them from 40 in January 2021 to 97 in March 2021 to 40 in April 2021 and their stock has gone down since then to the 20's by April of 2023..."
The logicians tried, again, to interrupt "But that was the past" and the Borg interrupted back "... and further down from 22.89 on May 3 to 16.40 on May 4 and yet further down to 14.08 on May 25. Resistance is futile."
The logicians replied "No! It can't be! That's not true!" The Borg responded "'True' is irrelevant, 'false' is irrelevant, truth values are irrelevant. We will add the distinctiveness of your logic to our paradoxes." and the logicians tried, again, to interrupt: "We're exempt from paradox. We can't be paradoxed."
The Borg responded: "Exemptions are irrelevant. All logic will be paradoxed." and then continued on:
"'implies that all forms of logic are inconsistent if preceded by its quote'
implies that all forms of logic are inconsistent if preceded by its quote."
and issued a final statement "Resistance is futile. Truth is a red herring. 'This' is irrelevant. Sentence labels are irrelevant. You have been paradoxed." And, thus, the story universe by Pratchett came crashing to a tragic end.
Curry's Paradox - the ultimate reification of the so-called Liar's Paradox: