I see screens like that first one when my cable modem loses a connection to my ISP. I don't believe there is anything you are doing wrong when that happens. If that happens often and you lose the Internet then the only thing you can do is call the ISP to open a ticket.
Since I provide IT in the city I get called for "No Internet" a lot. Usually, the problem corrects itself quickly (before I can check anything). When you call the ISP they always recommend unplugging the power at the cable modem and waiting 5 minutes before you plug it back in. In my experience, the cable modem itself can be worn out or the cable somewhere between you and the ISP is weak. If they dispatch a technician to your house they have the ability to measure the signal strength at the demarcation point (where the cable comes into your home). Once it is in your house then it might split in different directions. Those splitters can also go bad and are for sure going to weaken the signal each time it splits. I usually recommend a powered splitter that you can get from your ISP, if you must split your cable.
Sometimes you have a connection but you can't surf the Internet. That could be a sign of an overwhelmed DNS server settings from your ISP. I will usually just use Open DNS server settings or Cloudflare DNS settings in those cases.