I just hit the Publish button on my Smugmug publish service right now and it’s currently exporting and uploading images. So it appears Smugmug itself is up and running.
In Lightroom Classic, if you choose File > Plug-in Manager, does it open OK and is the Smugmug publish service listed properly? Does the Updates section have a Check Now button? My Smugmug plug-in shows a version of 184.108.40.206.
If the problem persists, it would be worth contacting Smugmug support since they would know how to troubleshoot it more deeply. For example, they might ask you to enable the log recording options in the Debugging section at the bottom of the Smugmug plug-in options.
But because it’s an HTTP 404 error, there could be an issue with networking. So probably some things to try first are verify that Lightroom Classic has Internet access (for example, does the Map module work?); if not, make sure your computer has not lost Internet access (although if you’re posting here from the same computer, that means it does have Internet access).
If the rest of the computer is working fine on the Internet but a service within Lightroom Classic can’t connect, look for anti-malware or network firewall software that might be blocking access to specfic processes or ports. But again it is Smugmug who would know what ports their plug-in uses.