Based on things I read recently, I think I can now expound on what I wrote in the comments last year. I'll explain what I believe the mishna in Sotah 3:4 means, which from I gathered, is easily misunderstood by some, hence the mistranslation of that poster into Italian of "פרושים" into "Pharisees". The relevant section from the mishna reads:
"הוּא הָיָה אוֹמֵר, חָסִיד שׁוֹטֶה, וְרָשָׁע עָרוּם, וְאִשָּׁה פְרוּשָׁה, וּמַכּוֹת פְּרוּשִׁין, הֲרֵי אֵלּוּ מְכַלֵּי עוֹלָם"
"He would say: A foolish man of piety, and a conniving wicked person, and an abstinent woman [perusha], and those who injure themselves out of false abstinence; all these are people who erode the world."
The commentators - including the translators of Sefaria's English gemara - properly understood the mishna to referring to people who who injure themselves, but why would such people be referred to as "prushim", the famous title of the precursors of the later generations of Chazal, the Orthodox-like sect who butted heads against the Sadducees, Baytusees, early Christians and probably other cults as well? Moreover, if "prushim" has a bad connotation, why would it be used to define some generations of Chazal?
Therein lies the answer. Eliezer Finkelstein explained in his book "Haprushim V'Anshei K'nesset Hagedolah" (The Pharisees and The Men of the Great Assembly):
"היחס של כת הפרושים לחסידים הראשונים עדיין מעורפל ומסובך הוא. כידוע כינו הפרושים את מיסדי כתתם "חסידים הראשונים". כן מכונה יוסף בן יועזר "חסיד שבכהונה" (מ' חגיגה סוף פ"ב), בוודאי על שם שנתחבר אל כת החסידים, אעפ"י שרוב הכהנים היו ממתנגדיהם. לפי ענ"ד מעולם לא פסקו הפרושים מלהביט על כתתם ככת החסידים, אלא שמתנגדיהם התחילו לגנות אותם בשם פרושים, לומר "כופרים". המלה פרושים משמשת במובן העתיק והמקורי הזה עוד בספרות הרבנית, עי' תוספתא ברכות פ"ג הכ"ה "שמונה עשרה ברכות שאמרו חכמים כנגד שמונה עשרה הזכרות שבהבו לד' בני אלים כולל של מינים בשל פרושין..." במקבילה בירושלמי (ברכות פ"ב ה"ד) "ותני עלה כולל של מינים ושל רשעים במכניע זדים...נראה לענ"ד שגרסת התוספתא עיקר, ושצריך לומר כאן פרושים, כי איך אפשר להאמין שמעתיק, המוצא בנוסחאתו את הגרסה פושעים בברייתא זו, ימחקנה ויכתוב תחתיה פרושים...אלא שיש לבאר כאן את המלה פרושים במובן של "חיצונים"...נמצינו למדים שהשתמשו בביטוי פרושים במובן של כופרים עוד בזמן התנאים...ומזה יש ללמוד עוד שכת הפרושים נקראו בכינוי זה על ידי מחרפיהם, הם הצדוקים, ורק אחרי דורות התרגלו גם הם עצמם להשתמש בתואר זה..."
Translation: "The relationship of the Pharisee sect to the Early Pietists is still unclear and complicated. As is known, the Pharisees called the founders of their sect "Early Pietists". So Yosef ben Yo'ezer is called "the most pious among the kehunah (priesthood)" (Chagigah end of ch. 2), likely because he joined with the sect of the Pietists, despite the fact that most of the kohanim were among their opponents. In my poor understanding, the Pharisees never stopped seeing their sect as the Sect of the Pietists, but their opponents began to insult them by calling them the Pharisees, meaning "heretics". The word Pharisees (prushim) was used in its ancient and original meaning also in Rabbinic literature, see Tosefta Brachot 3:25 "Eighteen Berachot (blessings) that the Sages have established [for the prayer of Shemoneh Esreh have been established] corresponding to eighteen mentionings [of God’s name] that are in [the chapter of Tehillim that begins with] “Ascribe to God, children of princes…” (Tehillim 29) And [a person] should include [the Beracha against] the apostates into [the Beracha] of the heretics (prushin)1..." in the parallel source in the Yerushalmi (Brachot 2:4) "and it was taught in a baraita "and [a person] should include [the bracha] of the apostates and that of the evil men in "Subduer of the insolent"...in my poor understanding, it seems that the Tosefta's version is the most correct version, and that one must say here "Pharisees" (prushim), because it would be hard to believe that the scribe, who found in his manuscript the version of "sinners" in that baraita, erased it and wrote instead "Pharisees" (prushim)...therefore we must explain that the word Pharisees means "externals"...from here we learn that the in the past, the term Pharisees was used per the meaning of heretics, even in the time of the Tannaim...and from this we may further lean that the sect of the Pharisees were called by this title by their cursers, the Sadducees, and only after some generations did they get used to calling themselves also by this title..." (pg. 33-34, footnote 119)
So in other words, the old meaning of the word "prushim" was a reference to heretics, people who made themselves external, meaning, people who left the orthodoxy, the mainstream. In the Sadducees' view, the Chachamim (sages) had left the orthodoxy. Finkelstein notes (pg. 25) that the Sadducees thought that Torah authority rested only in the hands of the Kohen Gadol and his men, no one else, which stands in contrast to the sages' tradition of Moshe receiving the Torah at Sinai and passing it down through the generations to many non-Kohen Gedolim people - Yehoshua (from the tribe of Efraim), etc. The one person who stands out in this list is Shimon Kohen Gadol, who was both a KG and a leader among the Pharisees/sages. For what the Sadducees perceived to be the Pharisees deviating from the proper halachic and hashkafic views, they felt they deserved to be deemed heretics.
During this era, the teachings that used the negative meaning of "prushim" began to pop up, because that's what the word meant at the time - to all sects. In Sotah, in the Tosefta in Brachot and in other places, such as in the Avot D'Rabbi Natan section that recounts how the Sadducees and Baytusees came to be. The term there is also "pirshu" - "[they] left", clearly because they left the mainstream of the sages and set up new sects.
Later on, though, the name stuck somehow to the Pharisees, and they adopted it themselves. It was at this time that they created positive meanings for the term, for example, Sotah 9:15, Vayikra Rabbah 24:4, and so forth.
The older definition was still in occasional use, though, for example, Rambam, Hilchot Teshuvah 3:11, but in general, the term evolved to become a positive one.
Note: Based on this, definition, it seems that the reason that the authors of the NT constantly used the term "Pharisees" to refer to the sages was because they considered them heretics. If any of the times that the NT's Jesus says the word "Pharisees" in reference to the sages (for example) is an actual quote, then that means that Jesus was not of them (a contradiction to the modern claims among some that Jesus was a Pharisee), for if he was part of them, he would not insult them so (I believe that even in the most harsh of debates, the Pharisees didn't call one another so).
1 I edited Sefaria's translation per Finkelstein's understanding.