I intermittently fast already - always have as I don’t eat breakfast - so for me the only way to lose weight was eating smaller portion sizes and cutting out starchy carbs entirely - no bread, pasta, potatoes. I would occasionally have a wholewheat wrap or ryvita. Also increasing protein a lot and cutting down on fat - so no cheese, milk but plenty of full fat greek yoghurt.
Doctors are supposed to treat the symptoms of peri now, so if you’re being fobbed off, go back and advocate for yourself more. It’s infuriating that they would be dismissing you. Exhaustion, rage, mood swings, hot flushes, insomnia are all common and should be taken seriously. Ask if your practice has a menopause specialist - might be a nurse / nurse practitioner - and speak to them. That said, if you don’t have the symptoms there’s no point getting HRT - it won’t help you lose weight on its own.
Try meal replacement shakes and / or protein shakes for at least one meal a day. Huel black is a good one and is affordable, but there are plenty out there. Note meal replacements and protein shakes are not the same so choose the type suited to your overall diet to ensure you’re not lacking anything important. They are also UPFs so bear that in mind.
The hand portion method is good for helping you stick to the right amount of food. NHS Diabetes pages have lots of info, or just google it. Eating little and often within your window (if doing intermittent fasting) will help maintain blood glucose so you don’t feel hungry - as will upping your protein hugely.
Or give ozempic or one of the others a go. I haven’t myself but know some friends who have and they say it really works. But of course only consider this through proper medical channels!