How do I clear all intervals?

Store 'em in an object. Since you're the only one making these intervals, and you know what they are, you can store them and later mess with them as you wish. I'd create an object dedicated for just that, something like:

var interval = {
    // to keep a reference to all the intervals
    intervals : new Set(),
    
    // create another interval
    make(...args) {
        var newInterval = setInterval(...args);
        this.intervals.add(newInterval);
        return newInterval;
    },

    // clear a single interval
    clear(id) {
        this.intervals.delete(id);
        return clearInterval(id);
    },

    // clear all intervals
    clearAll() {
        for (var id of this.intervals) {
            this.clear(id);
        }
    }
};

Your first question might be

Why make a separate object for just that?

Well Watson, it's to keep your hand-made intervals related to your plugin/project away from prying eyes, so you won't mess with other intervals being set in the page not related to your plugin.

Yes, but why can't I store it inside the base object?

You most certainly can, but I think this way is much cleaner. It separates the logic you do in your base with the weird timeout logic.

Why did you store the intervals inside a Set and not an array?

Faster access and a little bit of cleaner code. You can go either way, really.

You can find the "highest" timer identifier by creating a new timer that does "nothing" (by giving it an empty function to run, scheduled to run decades in the future), and then clear every timer between ids 1 and that identifier, like so:

// Get a reference to the last interval + 1
const interval_id = window.setInterval(function(){}, Number.MAX_SAFE_INTEGER);

// Clear any timeout/interval up to that id
for (let i = 1; i < interval_id; i++) {
  window.clearInterval(i);
}

However, note that this is not guaranteed to work: the HTML standard does not actually prescribe how timeout/interval identifiers get allocated, so the assumption that we'll get a reference to the "last interval identifier + 1" is merely that: an assumption. It might be true for most browsers at the time of this answer, but there is no guarantee that's that will still be the case even in the next version of the same browser.