Through known chat services, other users should not be able to obtain that information.
However, without knowing the other site it maybe trickier. The only reason why I say this is that if it’s a unknown site for all I know the person could be an admin/owner of the site, which probably can find those details in the log. Now with that being said, taking that IP address and doing something on your connection and being successful is slim if you don’t have your modem broadcasting it’s config page to the public. By default all equipment is never set to this.
“Connected to device, cannot provide internet” almost sounds like either A. your internet is down. B. You provided the wrong passphrase to your equipment or C. The equipment is having an issue.
I would reboot all your network devices and try again. I don’t see you mention any other device that connects, so I am going under the assumption you are wifi only on it. After rebooting if you have the issue, I would suggest that you contact your internet provider, since they could be having issues that maybe causing your problems.
If other devices are connecting, but not that one, I would suggest to reboot the affected device then.
This could very well be a problem. The past issue I had with my internet it was dropping heavily in the morning only. ISP came out and my ground level box had a knick on my line for the drop and what was happening was the condensation in the morning from the grass was building up on the line and causing water to enter the knick on that line.
Sounds like what you are describing with a similar looking issue on your line.