There has been movement at the station. Reposting an update on how the negotiations are going from this answer on meta.StackExchange, which also gives details on other updates over the past fortnight.
2023-06-26: Philippe takes over as primary negotiator on SE's side. Mithical, one of our representatives, dropped a list of our demands and updates on progress (link requires Discord access to work, and being in the previously linked server):
Demand: The prohibition on moderating GPT content must be retracted.
Progress: We have tentatively established a broader replacement interim policy, that will allow moderators much more room to remove AI content (although not to the same extent as before). This policy will go into effect upon release, replacing the current private policy. More permanent standards will be established by a working group of moderators and users who are active in removing gen-AI content, in a private Stack Overflow for Teams instance. Information on how to be invited to the Team will be available when we move along a little further in the process.
The replacement policy will be based on "strong" and "weak" heuristics, with guidelines on removing based on which heuristics are present. Moderator judgement calls will still be required. These standards will be open to revision as technology changes and data is gathered on identifying AI-generated content.
Demand: The private policy on GPT content that was issued to moderators must be revealed publicly.
Progress: Stack has agreed to release it publicly on Meta. However, it will be released with a disclaimer (as-yet unwritten) stating that they do not plan on releasing all moderator policy guidance publicly, but are doing so in this case. This disclaimer will have to be approved by reps before it's posted. This will be released after the new interim policy goes into effect.
Demand: The data dumps must be re-enabled, and SEDE and API access guaranteed.
Progress: We have reached the agreement below. This commitment will be announced publicly by Stack Exchange, Inc. (I don't know exactly when).
Agreement: Stack Exchange, Inc. commits to: Continuing to operate the data dumps; continuing to provide Stack Exchange Data Explorer access; and continuing to provide API access. All of these will remain operational and free of charge for individual network users, for the foreseeable, long-term future. For companies and organizations, other terms may apply.
Demand: Stack Exchange, Inc. must communicate, gather feedback, and act on that feedback before making major policy or software changes to the public platform.
Progress: The representatives from Stack Exchange, Inc. have indicated that they are willing to add a stipulation that binding policy changes (i.e. anything tagged moderator-agreement-policy) go through a mandatory seven-day review period by moderators. This is not yet finalized, and we have not yet reached a conclusion on software changes.
Stack has also indicated that toxicity in staff/mod communication is a sticking point in increasing this interaction, particularly in the Teachers' Lounge. While I disputed many of the examples that were brought, some examples were brought that did cross the line. I've handled those cases, and I will be speaking to the other Teachers' Lounge elected moderators about making sure this is addressed more consistently in the future.
Issue: Stack Exchange, Inc.'s data analysis is flawed.
Progress: The representatives from Stack have indicated that their experience on the network during the course of the strike has shown that their internal estimates were inaccurate, although not yet convinced that they are as inaccurate as we (the moderators and community) believe. They are not willing to retract the policy change based on that alone.
Issue: Moderators were not spoken to by CMs when their actions were in doubt.
Progress: Stack has stated that their internal guidance was to almost never consult with moderators about actions taken, due to a belief that moderators want to moderate and are not interested in justifying their actions to staff. We have established that the vast majority of moderators would welcome any questions about their actions and be more than willing to explain - or, even better, to train CMs in how to figure out why those actions were taken. Stack Exchange Inc. will revise their internal guidance to reflect this.
Issue: Stack Exchange, Inc. made inappropriate comments to the press.
Progress: We are debating this issue and have not yet reached a conclusion. Stack is so far unwilling to agree to a blanket policy of "no comment" when asked for comment on anything involving moderators; we are considering what our options are here. Stack Exchange, Inc. would like to keep open the option of commenting on general moderator actions not taken by an individual; the representatives are pushing for Stack to refrain commenting even about groups of moderators. Stack has also indicated that they think it would be unfair for the company to be bound to not comment while individual moderators are free to comment, citing my own personal statements to the press. I've reminded them that they are a billion-dollar company, while we are a group of volunteers.
Issue: There is no recourse if Stack Exchange, Inc. breaks the Moderator Agreement.
Progress: Frankly, there's been no progress. It was floated that a group such as the Moderator Council should have the authority to rule that an action taken by Stack Exchange, Inc. broke the Agreement, and is so rendered null and void; however, the Mod Council is currently defunct and is unlikely to be revived. We have not resolved this to any degree; suggestions are welcome.