I had a look in the Windows Firewall, and scrolled down to NzbDrone, and it was only checked for Private, not Public. After allowing it on a Public network, I was able to connect to Sonarr on my networked computer without issue.
I’ll have to see what went wonky with my network and what changed, because I didn’t change anything myself - wondering if my network somehow reset and the first person to turn on the computer picked a different setting or something.
Regardless, my issue is solved and I thank you for the help!
Edit: I figured out the problem (just in case someone searches the forums and has a similar issue). Someone had changed a network setting on my HTPC (running W 8.1) and it changed my network from Private to Public. I fixed it by going to PC Settings > Network > Click on your Network > Set “Find devices and content” to the On position. I then changed my Firewall rules back to normal.