The standard actually is the plaintiffs are likely to prevail on the merits (not "might"-- it's probable per the judge), and in practice a preliminary injunction hearing in a major case can take the form of a mini-trial. The judge wrote 155 pages that, at first blush, appear to be a very serious and thoughtful effort. The judge summarized on page 154 thus:

"The Plaintiffs are likely to succeed on the merits in establishing that the Government has used its power to silence the opposition. Opposition to COVID-19 vaccines; opposition to COVID-19 masking and lockdowns; opposition to the lab-leak theory of COVID-19; opposition to the validity of the 2020 election; opposition to President Biden’s policies; statements that the Hunter Biden laptop story was true; and opposition to policies of the government officials in power. All were suppressed. It is quite telling that each example or category of suppressed speech was conservative in nature. This targeted suppression of conservative ideas is a perfect example of viewpoint discrimination of political speech. American citizens have the right to engage in free debate about the significant issues affecting the country." [1] (emphasis mine)

[1] https://storage.courtlistener.com/recap/gov.uscourts.lawd.18...