Try magnesium glyclinate and physillium husk for the constipation. Also make sure you're taking a good multivitamin and eating at least 1250 kcals per day, drinking loads of water and getting enough protein (minimum of 1g per KG bodyweight).
I've lost almost three stone in 4 months on Mounjaro, currently on 10mg.
As an example of what I eat in a day, here's today:
Breakfast - 1 slice of wholemeal toast with 2 scrambled eggs (made with a splash of almond milk and 5g of real butter), cup of coffee with sweetener and almond milk
Lunch - chicken thighs marinated in fat free greek yoghurt, garlic and spices, cooked in the air fryer, in a pitta with salad, onions and light mayo
Dinner - mayflower chicken curry (massive 400g portion), onions, peas and mushrooms with air fryer chips (small portion)
Snacks - iced coffee made with almond milk (I use the no sugars Alpro) and 10g of coconut protein powder, Options Praline hot chocolate (made in my Hotel Chocolat Velvetiser) and a Coconut Almond protein bar.
According to Nutracheck, I'm on track to finish the day at 1356 kcals and 110 G protein. This is roughly where I'm at most days and I'm losing approximately 3lb per week on average. Crucially, it hasn't always been linear though. My weight has gone up, down dramatically and frequently stuck at the same. The overall picture is downwards, albeit (fairly) slowly.
For me the amazing thing is how effortless it's been. I'd never have been able to stick to such a deficit for any length of time without the medication. I also feel great on it - less anxious, calmer and more focused.