It'd be nice if the proxy manager could be ran from within a subfolder like many other UI tools do

[codebymikey]

Reopening since #2577 was marked as stale.

It's simply a matter of ensuring all the assets are loaded relative to the current path rather than being absolutes.

If necessary, we might also need to expose a variable for the web path to use similar to MailHog's MH_UI_WEB_PATH