This is very similar to SERVER-46932, but new in 4.4.15, and only exhibits when TLS is enabled in the server.

Here's an example of the new message (which prints even with --quiet):

{"t":{"$date":"2022-07-05T17:20:33.332Z"},"s":"I",  "c":"NETWORK",  "id":5490002, "ctx":"thread1","msg":"Started a new thread for the timer service"}

Looking through the commit history, I think this was introduced by https://github.com/mongodb/mongo/commit/65134ea4e05c6c6d2647186782775ae0cdeb712e (which means it'll probably affect 6.0 also).