Easiest answer: You really can’t mark everything on Discourse as “read” with one button.
In general, topics that contain messages you haven’t looked at will show in a brighter (or darker, depending on theme) text color. There’s no way to change this without actually reading the threads.
There are tools to prioritize topics you are interested in as your Watched and Tracked topics. At the very bottom of each topic there is a button that shows your interest level in the topic. You can click it to change: mute the topic, watch it, or track it. This will build a list of topics with read pointers under your “Unread” tab at the top.
In your Unread tab, there is a “Dismiss” button on the right to reset your pointers as if you read all your tracked topics, but they will build up again as topics get more replies.
Discourse will automatically track topics you spend a lot of time reading, and you can adjust this in preferences under your profile.
I may be mistaken about what actually shows up in your Unread tab - whether it’s Tracking or Watching - I generally don’t use Unread since I am always looking at most new messages under “Latest”. In most cases, Discourse is set up to learn your reading preferences and you generally don’t have to micromanage it.
I believe you could ignore “Latest” completely, just marking only the topics you want to read and living in the “Unread” tab, which can be set as your default under Interace in your preferences: