Couple points from reading the thread:
For library wifi, like someone has mentioned, do note that these public wifi services are usually very slow since there are probably hundreds of people on the wifi access point. It happens a lot in public wifi places, Starbucks, hotels, etc. They can be so slow that even their own splash page couldn't load. So this could've been nothing to do with your laptop at all. If your laptop can connect to any other wifi access points just fine, then it could be the issue is just the library's wifi access point is too congested. Nothing you can do about it.
Good point, however one of the reasons I love this library is that there aren't that many people here. And I suspect there are less than 5-6 people using the Wi-Fi at any given time. (Lot so families come in to get books, but this is not your standard "Internet cafe" type library.)
Last night after I left the library, I went out to my car and the best I could get was 2-bars on my iPhone.
I drove down the road a quarter of a mile to a gas station, and same issue.
Then I went over to an AT&T store and lamented to the store manager - who was a pretty cool guy - about my woes.
Of course in the AT&T store, I had 3-bars, so that didn't help.
He showed me how to reset my network settings, and I'm not sure if that helped, but I did have 4-bars in my car outside the AT&T store.
I think I checked it this morning when I went across town to a pharmacy, and there I had 4-bars.
Now back at the library, I am tethered to my iPhone, and I have 1-bar and sometimes 2-bars, and in my last two responses, my Internet connection has dropped 5 times in 5 minutes.
Not sure how this is possible, but apparently there is some blackout spot in a mile radius of this library which is VERY frustrating since that will never get fixed.
(And which is why I need the library Wi-Fi to work!)
Let's hope Mojave fixes my issues...
Another troubleshooting tip, install a chromium based browser. It's sad, but more and more web devs are basing compatibility off Chrome instead of HTML standard.
That is sad.
Meaning many sites (even splash pages, those are web sites), tend to work correctly with chromium based browsers.
I didn't know this.
Google Chrome is the obvious one, but you can also try Brave or Microsoft Edge. Leave it at default setting, make it your default browser and see if the splash page works.
I'm still trying to understand how you can use Microsoft Edge on a Mac? I guess it isn't like Internet Explorer, eh?
As for macOS upgrade, imo you just have to check if you still use 32bit apps or not. If yes, go with Mojave. If not (all 64bit), go with Catalina. Quite simple. My 2012 mini is running Catalina just fine, so I bet your MacBook Pro can run it great since it has much better spec.
How can I easily do an inventory of all of my apps and determine if they are 32-bit or 64-bit?
As far as your advice about Catalina, it sounds like some earlier posters strongly advise against that!
I hope Mojave fixes things for the next year or two, and I'm going to start another thread about newer OS's, since it sounds like my conception of a computer OS is changing for the worse.