A few thoughts off the top of my head. Apologies I don’t have the time to organize these a bit more for you today:
The check runs from your browser so it’ll be different on each device you run it from (or, at the very least, each connection you try it from).
The check for whether the admin is throttled is new, but it doesn’t mean you weren’t being throttled before - just that you weren’t aware of it. The idea was that now the setup checks give an indication when this situation is detected.
The inconsistency may also just be due to your IP address expiring out from the brute force IP table (it’s ~25 minutes IIRC but I don’t recall all the logic behind it off the top of my head).
Given your network topology, you may want to install the BruteForceSettings app and experiment with whitelisting your home router IP address as a start:
The other possibility is that there is something weird about your network topology where you’re sometimes going through your router… and other times not (Proxy ARP comes to mind).
One way of avoiding having your connections bounce through your router’s when you’re local would be to use split DNS. That way when you’re on your local network you’d not go out to your WAN IP address and back. It’s possible that’s creating some weirdness (often it doesn’t even work on consumer routers or, in my experience, even when it does it’s flaky or impacts performance.