AWS Secrets Manager can’t find the specified secret
ok, so the trick was to specify ARN explicitly. Instead of just providing secret name you should use full identifier
-ID0o2R suffix at the end of secret name.
It's still not clear for me why for some variables it works without it.
However, if your secret has a name that ends in a hyphen followed by six characters (before Secrets Manager adds the hyphen and six characters to the ARN) and you try to use that as a partial ARN, then those characters cause Secrets Manager to assume that you’re specifying a complete ARN. This confusion can cause unexpected results.
So as you can see from my variable name containing a hyphen Secrets Manager had hard times when resolving it by short name
Secrets Manager tries to do partial ARN matching when you do not specify the GUID on the end of the ARN. However, it is imperfect because partial ARNs could collide. If you are fetching secrets within the same account, you can just use the secret name (the part after secret: and excluding the dash 6 character -GUID) instead of the full ARN. But using the full ARN, when you have it, is always best.