Why WiFi-Manager directs to 192.168.244.1 instead of 192.168.4.1? (SOLVED)

This is the IP address of the Blynk cloud server in Frankfurt, so that’s the correct result.

With your other computer, and possibly your NodeMCU, it’s seeing what I assume to be an internal IP address. What IP address range are you using for your home network?
You mentioned that the computer that gives the correct IP address is connected via a cable. Is the other connected via Wi-Fi? if so, what happens of you connect that via cable and disable Wi-Fi?

Do you have any weird and wonderful network setup - private DNS server, local routing table entries on the “strange” PC, multiple DHCP servers etc?

Pete.