I've recently upgraded Jenkins to the latest stable version Jenkins 2.361.1 and latest Embeddable build status plugin version 255.va_d2370ee8fde (from 2.0.3).
And now all the badges on Confluence and Bitbucket show grey fallback icon "build not run"
I have double checked that all the links are double encoded, e.g.
https://jenkins.domain.net/buildStatus/icon?job=my-branches%252Fmain!
I also tried with %2Fmain but to no avail.

Jenkins and Confluence are connected over crowd2 plugin (that was also updated to version 3.1.2), so there are no users in Jenkins as such, auth is managed by Confluence/Jira

My understanding is that Jenkins and Confluence can connect just fine, otherwise I wouldn't even see the fallback icon.
Current Authorization method is "Logged-in users can do anything" and " Allow anonymous read access" is disabled. If I enable it - build status icons start to work, but I don't really want to do that to be honest.

I also asked on the forum and it was suggested that

there should be a new permission you can enable that allows badges only

but I cannot see it.