Earlier quoted context omitted.
Why not ask direct & clear then? I also think it sounds disingenuous. This kind of passive-aggression is what “cracking the whip” feels like for employees.
How do you get more clear? When I say "If there's anything I can help with please let me know." that's what I mean. The misinterpretation is because of overthinking, not because of vagueness. I can reassure the person if they want, but they have to tell me they need reassurance before, or I have to at least detect they're uncomfortable. I'm not gonna go to every employee and say "ok just so you know, I'm not thinking…
There's also the reality that, when corresponding with your employer, it's sort of like talking to the police: anything you say can and will be used against you.
If my manager had a "hey, what's going on?" conversation with me out of the blue, my immediate reaction would be concern. I honestly believe that my manager is a good guy who wants me to succeed, and I'm still very cautious about what I say to him. I know that I can never un-say anything. Also, losing this job would be difficult. Though I am a software engineer and could find work relatively quickly this would put me in a very difficult situation due to the US health insurance system and my wife's serious illness.
I would suggest:
1. In-person or video chats instead of email/slack when possible. Written words tend to be so much more prone to misunderstanding and can be used against a person more readily.
2. When possible, regular scheduled informal reviews with your reports, instead of unscheduled "what's going on?" queries. I've never understood why managers don't make time to talk to their reports one-on-one at least once a month. They could be short 15 minute conversations!