Thank you so much for that troubleshooting step. It turns out that, for some reason, I cannot get to that site from my ISP.
I just switched from Xfinity (public IP) to fiber (CG-NAT), so I'm not sure if the CG-NAT has something to do with it. I still have my Xfinity service for a couple of days, and when I switch my WAN connection back to Xfinity I can download the plugin without issue.
It was extra confusing because I was connect to my work via a VPN and the file was downloading fine on my Windows machine. Once I used a device on my local network I couldn't even reach https://pkgs.tailscale.com.
Super odd, I think I'll file a ticket with my ISP.
In any case, thanks for the help!