Is there a noun that means "someone who's in on a secret"? There are words like accomplice and co-conspirator for people who take part in clandestine activities, but I failed to find one for people trusted with a secret, but not actively participating in anything.
A person with whom one shares a secret or private matter, trusting them not to repeat it to others: a close confidante of the princess
One who has special knowledge or access to confidential information. American Heritage® Dictionary
A person who is being formally accepted or who has been formally accepted as a member of a group or organization
(adj.) Instructed in some secret knowledge M-W
A person to whom something is confided or entrusted; He's the repository of many secrets. M-W
Originally conspirator simply meant someone who breathed with you; but words change and as you say, it desn't mean that now.
Conspirator is a suitable synonym
One of a group that acts in harmony https://en.wiktionary.org/wiki/conspirator
You might consider inner circle, which implies a select few who possess special knowledge or power that is not available to others.
: a small group of people who lead a government or an organization or who are close to its leader
While this definition speaks of an organization, to me the term can equally apply to unofficial groups of people that can't be necessarily described as an organization—the group can be defined simply by who knows a shared secret. A native English speaker would definitely accept, for example: "Jerry hasn't been approved by everyone to be in the inner circle yet, so we can't tell him about George's double or he'll figure out it's time travel, not just teleportation!"
Since you did ask for a single word, you could simply call folks in the inner circle inner-circlers. Though likely a unique word, I think this would be well-understood by native speakers.
You could say "inner circle member" if you're willing to use a phrase rather than a single word.
Also consider informal phrases such as She's cool or He's one of us.
These tend to be used to indicate to someone that a person is already privy to any secrets that someone might wish to discuss, so it is okay to talk about secrets with them present.
Sophie (eyeing David): So I want to talk to you about that (secret) thing...
James: Don't worry, David's cool, he's one of us.
Sophie: Ah. Then I have some questions about the bank robbery...