It’s working as expected now. The required network-manager interface was connected to my snap’s network-manager interface (see previous post), but I tried disconnecting from the network-manager:service slot then re-connecting it, and now it’s working.
On another note, is there any way to auto-connect this interface instead of having the user who installs my snap have to do so? Or are there plans for a permissions/interfaces request prompt when a user installs a snap (similar to Android) so they can be auto-connected at that time?