How long does it take to recover from a binge?

Your weight is always accurate, minute by minute.

The problem is knowing how much of your suddenly added weight is temporary water retention and temporay extra digestive system contents, vs. added body fat. I'd suggest not worrying about it, watching what happens on the scale as you get back on your healthy routine, and learning from that. Eventually, you'll have an intuitive understanding of how your body behaves.

For me, water weight loss, if it's from extra carbs/sodium from a high-eating day(s), is fairly rapid - couple of days, usually - but somewhat dependent on what I do. I'm emphatically not suggesting you try to rush it, I'm just reporting based on what I've observed. A bunch of things seem to affect the speed, in my case: Adequate vs. under-hydration (over-hydration is just a bad plan health-wise); sweaty exercise or none; even things like massages seem to make a difference. Really, though, don't try to game it. Just watch your body do what healthy bodies do, and learn from it.

Digestive system contents are also variable. There was some small-scale research suggesting that full digestive transit can take 50+ hours . . . but it's also highly variable from person to person and situation to situation. It may matter what foods the "binge" consisted of. Just watch what your body does, and learn from it.

Try to relax about it, and think of it this way: You don't have a "true" current weight. Over a day or a few, you have a current weight range, up and down a few pounds for various reasons, most of which are water and digestive contents, not fat gain/loss. Over weeks to months, your weight range shows a trend: The daily up and down bumps turn out to be bumps on a downhill slope when you're losing, on an uphill slope if you're gaining, and on more-or-less horizontal level if you're maintaining. That long-term trend, for a reasonably healthy person, is mostly about fat loss or gain. (Muscle gain/loss can contribute to a very long term trend, like months to years, but fat changes are usually faster/more material for most people.)

If you use a weight trending app (Libra for Android, Happy Scale for iOS, Trendweight with a Fitbit account, Weightgrapher, others), that can help you visualize the trend. Don't make the mistake of believing these things are a crystal ball, with infallible insights. They're just statistics. But they can be helpful. You need a month or so of daily weights (at a consistent time/conditions) to really begin to get anything out of them.

You might find this thread fun or interesting (it's a detailed report on an episode of seriously over-goal eating, and its aftermath):

https://community.myfitnesspal.com/en/discussion/10603949/big-overfeed-ruins-everything-nope

Also, if you truly had a binge, please try to figure out why: Have you set yourself too low a calorie goal to be sustainable? Losing slowly but steadily is usually a faster route than targeting a fast rate loss rate that you can't achieve in actual reality. Have you eliminated foods you enjoy, that you could fit into your eating in manageable portions to avoid cravings? Have you found how to stay satiated on reduced calories? Is the eating about some underlying problem (lack of sleep, stress, emotions, boredom, social triggers, etc.) that could be dealt with more directly?

Best wishes!