So the law they are suing over is here https://legiscan.com/CA/text/AB587/id/2599787

I think the part that they probably have issue with is the

"(5) (A) Information on content that was flagged by the social media company as content belonging to any of the categories described in paragraph (3), including all of the following:
(i) The total number of flagged items of content.
(ii) The total number of actioned items of content.
(iii) The total number of actioned items of content that resulted in action taken by the social media company against the user or group of users responsible for the content.
(iv) The total number of actioned items of content that were removed, demonetized, or deprioritized by the social media company.
(v) The number of times actioned items of content were viewed by users.
(vi) The number of times actioned items of content were shared, and the number of users that viewed the content before it was actioned.
(vii) The number of times users appealed social media company actions taken on that platform and the number of reversals of social media company actions on appeal disaggregated by each type of action.
(B) All information required by subparagraph (A) shall be disaggregated into the following categories:
(i) The category of content, including any relevant categories described in paragraph (3).
(ii) The type of content, including, but not limited to, posts, comments, messages, profiles of users, or groups of users.
(iii) The type of media of the content, including, but not limited to, text, images, and videos.
(iv) How the content was flagged, including, but not limited to, flagged by company employees or contractors, flagged by artificial intelligence software, flagged by community moderators, flagged by civil society partners, and flagged by users.
(v) How the content was actioned, including, but not limited to, actioned by company employees or contractors, actioned by artificial intelligence software, actioned by community moderators, actioned by civil society partners, and actioned by users."

Combined with this section of the bill

"(b) Actions for relief pursuant to this chapter shall be prosecuted exclusively in a court of competent jurisdiction by the Attorney General or a district attorney or by a county counsel authorized by agreement with the district attorney in actions involving violation of a county ordinance, or by a city attorney of a city having a population in excess of 750,000, or by a city attorney in a city and county or, with the consent of the district attorney, by a city prosecutor in a city having a full-time city prosecutor in the name of the people of the State of California upon their own complaint or upon the complaint of a board, officer, person, corporation, or association.
(c) If an action pursuant to this section is brought by the Attorney General, one-half of the penalty collected shall be paid to the treasurer of the county in which the judgment was entered, and one-half to the General Fund. If the action is brought by a district attorney or county counsel, the penalty collected shall be paid to the treasurer of the county in which the judgment was entered. If the action is brought by a city attorney or city prosecutor, one-half of the penalty collected shall be paid to the treasurer of the city in which the judgment was entered, and one-half to the treasurer of the county in which the judgment was entered."

Basically the law requires a full disclosure of all content moderation decisions and explicitly why they were made, and then gives incentive for various city DAs to bring suit by promising them a 50% cut of whatever money is made in the lawsuit.