Connecting my Pi to the interwebs through my computer should be easy, right?

NOPE!

Two hours of fiddling with badly-documented config files after I started, I can SSH in but not access the internet on the Pi. None of the guides seem to want to actually work...

Have you defined the gateway and dns in your net set?

Try this:
Static IP on Windows side
'Share' Network interface with Internet access to the interface the pi is connected to on in windows
Static IP PI side
Set default gateway to the windows machine pi side
Add search 8.8.8.8 to /etc/resolve.conf
???
Profit
Actually everything you need should be documented pretty well

Try connecting to your Pi through RDP (remote desktop). I tried it the other day with my Pi Zero W and Windows laptop (because it has Windows Remote Desktop Connection built-in). Worked like a charm, no lag whatsoever.

@hacker That needs an internet connection...

@Kimmax The computer isn't running Windows.

@wolt Linux, Ethernet and because the Pi's onboard WiFi isn't great.

No windows makes it even better!
Take pi steps as is.
I assume a debian based system.
Assign static ip to the interface the pi is connected on.
Important!
echo 1 > /proc/sys/net/ipv4/ip_forwarding (path is guessed, you may need to check that)
And than it depends on your setup. If you have the pi in a different subnet you may need masquerading (or SNAT) on the outgoing interface. If you have strict firewall rules you may need to allow the communications between the two interfaces too