Pumping iron can make you look and feel better at any age.
When I did a keto diet to successfully clear up my reflux, I lost muscle mass and ended up with shoulder bursitis. Since adding light weights and exercises from the physio, I solved the bursitis and carried on. Muscle mass feels so good.
It seems like you have a good coach that made you rethink something essential everyone (especially women) needs to do!
Great points, clearly highlighted the major benefits (and there is so many more!) - I particularly like that you mentioned the confidence. My almost 2 decades of working with people on their health, wellbeing and fitness has by now shown me that this confidence is exactly the best thing anyone can get from lifting heavy.
And also as a coach there is almost nothing better then teaching a deadlift to a 40+ year old woman who is scared of anything heavier then 20 kg, and by the end of the session she is ripping off them 50+ kgs and saying "Wow, I did not know I am this strong!".
Little tidbit of mine, if I may:
Make sure to not confused "weightlifting" (the sport) with "weight lifting" (alternative wording for strength/resistance training). Unfortunately, I have seen in the past (especially around the topics of strength training and lifting weights with "non"-traditional populations like children, elderly, and yes, also women) people go onto quite unnecessary disagreements about the use of either.