I don't have any advice regarding peri menopause but I did experience hormonal shift when I weaned my 2 year old a few months back. Mostly feeling depressed and like I lost something ( my nursing happy hormones). We were only doing morning nursing so weaning was very gradual but still felt the shift so I can only imagine that if you were bf frequently and then drastically reduced feedings then there would definitely be hormonal changes. And of course everyone is affected differently. When I googled for tips on dealing with weaning depression I found an exercise program that helps with hormonal issues called T-Tapp. Although I did not do it while feeling depressed I have tried a few times recently and I can see that it could've helped in feeling better sooner. The most important thing I did do was give myself enough time to adjust and even though it felt like I would never feel like myself again it was helpful to just know it was a normal reaction and it would soon pass.
By the way I'm very impressed with 3years! Way to go!