You sound paranoid. There’s nothing wrong with a 20-something admitting they need a bit of a rest after working really hard for a few years.
I’ve had an employee tell me they’re exhausted and need time out and I definitely didn’t “propagate need to my network” about them. That would be a serious breach of trust. I’ve also hired an engineer who told me they just came off a burnout and they were great.
This fear of vulnerability is part of the problem - it’s ok to be burned out and need a bit of a rest.