The website at this time presents a list of people whom have been active in chat recently. The website doesn’t give the full list of viewers out. The first party/unprivileges user offering is very different to what the API provides
In theory, you only need to get Mods/VIPS for a channel once (and/or periodically) then use EventSub to keep up to date with changes. You wouldn’t be geting roles each time you got the list of users in a given chat. So you wouldn’t burn through the rate limit as you suggest.