Not to put too fine a point on it but… Yes.
Regardless of whether Twitter allows "good bots" to continue to post for free, it seems reasonable to assume that some amount of work would have to happen to get that "good bot" designation, and with over 100 Twitter accounts, that's a lot of work for what is, unfortunately, not a large avenue of engagement for the sites.
So, TL;DR: As of 8 Feb 2023, the bots have gone silent, network-wide. The integrations have been removed and we no longer maintain or support those bots.
Some data on Twitter numbers
Even our oldest sites, the other two in the trilogy, Server Fault and Super User have under 1000 followers (986 and 687, respectively), and most of their posts garner fewer than 50 views each and few, if any, other interactions (likes, retweets, replies). This is all info that's publicly accessible if you head over to their feeds yourself. While I can't easily tell you how many people are coming to the sites through those links, I'm guessing it's next to none, and that even the people who might be… they'd likely be visiting the site anyway.
I went through the numbers for the 27 most-active sites. Among them, 17 had fewer than 1000 followers, 9 had 1k-2k and only our Salesforce Stack Exchange site had more than 2500 (2,709) but the 10 most recent tweets there had only 900 views. Speaking of views, 21 of the sites averaged fewer than 50 views per tweet (and 14 under 20) over their last 10 tweets. The most viewed site's tweets were Database Administrator's but that seemed largely due to a recent tweet being retweeted by the author of the answer and gaining over 1400 views alone.
Just to put things in scale - I'm by no means a Twitter maven - and I have the benefit of being an actual person instead of a bot - but my modest Twitter account with under 200 followers regularly gets better view numbers than these accounts - even when I'm not posting images of LEGO or food.
Yes, there may be the occasional tent-pole tweet that gets a lot of visibility but that doesn't seem to be the norm.
As you mentioned, we stopped creating Twitter accounts on site creation some time ago. Here's the requisite quote from Adam:
Not all sites have Twitter accounts. We stopped creating them for all public beta sites by default because a) Twitter sees very little engagement for us; b) Twitter-the-company started blocking new accounts for us (probably because it thinks we're bots?) and fighting that got too annoying and time-consuming.
We currently have about 100 accounts (excluding the manually controlled ones). Since we have 180 sites now, that means we're almost at 50-50 with sites having and not having them, so it begins to feel a bit odd to keep them up if we're not going to continue to create new ones… and it's questionable whether we'd be allowed to, considering the past.
On top of that, we've had community members frustrated with the selection of posts by the bots, we don't have easy access to remove tweets that are potentially problematic, and the bots occasionally decide to start tweeting Meta posts in addition to main site posts, which may or may not be intended (honestly, who knows anymore?).
The Community Team is focusing on engagement (one of our subteams is specifically called “Engagement and Enablement”) and getting people to visit the sites, ask questions, post answers and stick around, joining the existing communities is one of our priorities. After looking at these numbers and the sentiments about the Twitter bots in general, we don't feel like this is a good place to spend our time - and potentially our money, if we do have to pay for it. (And again, development costs aren’t free, anyway!)
There's a lot we're hoping to do in the future - we’ll be sharing more soon - but know that engaging and building communities is something we will focus on in the next year, so look out for that!