How fast can I expect to lose weight at 290 pounds, 40% body fat, and 38% muscle on a ketogenic diet?
If you go to the gym and eat right, very quickly. Since you already know your stats and follow keto, I will assume this. Since you have a high body percentage and weight you can get "newbie gains" easily. If the scale doesn't move, you're likely still progressing in terms of body recomposition.
With just diet? Still quickly. You'll lose a lot of water weight at first, and then have roughly consistent weight loss. The human body, especially large ones, already burns a stupid amount of energy just by existing. If you ever eat a carby meal, however, you can expect to gain a lot of weight quickly from water retention and bloat. Don't be fooled.
The only real way you can get a date is by taking your numbers and use an online TDEE calculator to find out how many kcal you burn with your activity level (Katch-McArdle is the most accurate). Then you can subtract say 750 from that and lose 1.5lbs a week. There's a million weight loss calculators online. If you count your kcal, no matter the diet, you'll lose the same.
Keto is great for all the reasons you likely already know, but any cheat meals will leave you feeling terrible. Stick with the diet for a month or two and you can begin cycling carbs without the dreaded keto flu.