I trialed drospirenone as my progestin (in Drovelis) and that has a diuretic effect and my thirst was pretty bad for a while. Taking electrolytes did help, although it didn’t totally eliminate it. It could be worth a try though. There are also gels and tablets you can place on your gums to increase saliva production and those help really well with dry mouth. They usually contain xylitol and sweeteners give me gut issues, so I only used those when the dry mouth was really bothering me.
Personally, I’m progesterone intolerant, but I’ve tried getting used to utrogestan a few times and I also experienced vaginal irritation (especially when I tried it vaginally, only a few times, since it caused way too much discomfort). Increasing my vaginal estrogen to more times a week during taking progesterone (orally) did help a bit. I also experienced extra vaginal irritation during drospirenone and I’m not sure if it is the progestogenic or diuretic effect. I stopped last week, because it also caused extra eczema (dry skin) and going to try dienogest next (I’m doing estrogen only for 2 weeks to get my dose right and to let the drospirenone (which has a long halflife) out of my system), so I’m not sure yet if that will cause the same issue for me.
I always use eye drops 3x a day, because since my pregnancies my eyes have been dry. The gel drops, I use the “hylo gel” (I’m in the Nettherlands myself) drops, work way better for me than the more watery drops, so a change in the sort of drops you use can make a difference.