For the first part, let's just say that when I was a member of lemmy.world and commonly made posts critical of the Israeli Genocide in Gaza, I started receiving e-mails on the e-mail address I used to register in that instance, in my native language, from a Tel-Aviv based organisation inviting me for an online "Learn about Israel" course. I never make my e-mail public and as far as I know only instance Admins have access to that data about users, not moderators.

Another example: you can find a ton of pro-Israel posts by gedaliyah@lemmy.world, a !news@lemmy.world moderator who also "strangely" seems to specialize in opinating about other Middle Eastern nations (mind you, this is so overt I actually doubt they're a paid state actor - probably just an amateur far-right Israeli).

I've also seen and received some weird moderation actions in lemmy.world forums - for example like a post where I pointed out somemebody else's link to an article about something in China was to a think tank which gets funding from the Australian Defense Department, was moderated as "misinformation" when the "About Us" page in that site says exactly that they're funded by the Australian Defense Department. More broadly, posts in lemmy.world forums that relate to geostrategical "adversaries" and "allies" of countries like the US seem to attract way more moderation actions than pretty much anything else but outright spam and trolling.

Hardly proof of an abundance of state actors there, I know, but definitelly strange.

Also, purely from a "good management" point of view, it makes sense for state actors to concentrate their efforts on the largest instance and the larger forums in Lemmy, especially in terms of getting positions with power such as Admin and Moderator.

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As for the rest, yeah, I should probably check votes when I spot a weird voting pattern.

I'm averse to checking people's voting because I feel like I should treat voting as a way for people to anonymously signal their opinion, but it does make sense to check it if I see what I think is an abnormal pattern.