There is a Police Scotland Bluesky account (@policescotland.bsky.social) but there are zero posts on it. The same goes for Lothian Buses.
Edinburgh Council has a Bluesky account (@edinburghcouncil.bsky.social) which appears to be a mirror of its X account. However, other council functions such as edinhelp and edintravel appear to exist solely on X.
LNER has a Bluesky account (@lner.co.uk) but it seems to be mostly mirroring just the marketing puff on its X account. Its X account seems to get the useful information - disruption, engineering works and the like. Its Bluesky account does say "Our live responses via Bluesky are limited, please contact us on another social media channel if you require support." Which isn't very helpful.
Traffic Scotland doesn't seem to have a Bluesky account.
That's just a small sample of "organisations which provide useful information and/or assistance".
I may be mistaken, but my understanding is that many organisations use consolidated social media dashboard tools to manage and co-ordinate their postings and associated communications (direct messaging and such like) across the current confusing melee of social media services*. If Bluesky requires yet another plug-in or equivalent in order to be integrated into their dashboard, many may simply not bother when it's probably already a non-trivial job keeping abreast of their existing interfaces to all the other purveyors of ragebait, and AI and HI** dross.
When a new entrant into the market comes along they very likely take a look at how many users they are acquiring and prioritise on that basis. For example, TikTok is reported as having ~1.6 billion active*** users, compared to Bluesky which, according to Wiki, has 1.5 million and falling (X is reported to have 561 million active users). It may also not help that Bluesky is regarded as having a predominantly lefty/liberal user base.
* Don't get me started on companies which choose to use Instagram as their primary or even sole communications channel.
** i.e. Human Intelligence. If such a thing can truly be said to exist on social media. He said, posting on an online forum.
*** For a given value of "active" - which I'm sure must be defined somewhere, otherwise the stats would be essentially meaningless...