The only other edition I found on hebrewbooks is a far more modern (1960s) edition of tikunei haZohar. In it tikun 20 is one line long. This is also repeated in the text of ha-zohar.com where tikun 20 is abbreviated and combined with 21. This is repeated on Torat Emet, wikisource, and many other places. While many of the internet sites are clearly copying from each other, there is a printed book and a digital copy (original website unknown) that have the abbreviated tikun 20. What happened to it? Was this dropped deliberately or is something else going on?
The tikkun in question in the original was the long version found in the Mantua edition. The Vilna edition of Tikunei HaZohar with the commentary of the Vilna Gaon mentions this in the main text at the end of the shortened version.
The 5th volume of Tikunei HaZohar with the commentary of Ohr Yakar also has the long version. And the long version is also what is referenced in Sefer Kisei Melech by Rabbi Shalom ben Moshe Buzaglo.
The tikkun is dealing with the various ways that the redemption can unfold, Moshiach ben Yosef, Moshiach ben David, the erev rav and the consequences of the redemption coming early, late or somewhere in between. It also deals with the subject of pushing the redemption.
It appears that the text was abridged sometime around or shortly after Shabbatai Tzvi. In context, it would appear that there was a concerted effort to limit public access to this text at the time.
The claim that this text was censored and that this is somehow related to Shabbatai Tzvi seems unlikely for two reasons:
The text is moved to tikkun 21 and not removed entirely (beginning on 48a in the 1740 Qushta edition)
The suggestion that this text be moved to tikkun 21 appears long before Shabbatai Tzvi. For example see this, but unfortunately the library scanned the wrong manuscript so ignore the link provided there...