I ride my bike to the barn, ride, and bike back again and from September - May this usually happens in the rain. I upped my raingear plan this year and am pretty waterproof with:
Decathlon waterproof breeches: https://www.decathlon.com/collections/horse-rider-gear/products/womens-horse-riding-waterproof-warm-and-breathable-jodhpurs-kipwarm?
Waterproof jacket from Decathlon (bonus reflection strips for my bike ride home at night): https://www.decathlon.com/collections/horse-rider-gear/products/horseback-riding-warm-waterproof-jacket-500?
The jacket is great too because it has a high neck so no water can drip in through the neck (there’s also a packable hood).
Cheap tall leather boots are my go-to in the rain too - no water soaking through the ankle boots and half chaps.
I have also had the Mac-in-a-pack pull on pants on my list to try, though I’m not sure if you can ride in them: https://www.amazon.com/Mac-Sac-Unisex-Waterproof-Packable/dp/B07C9X17TW
And I have two light rain jackets - one stays in my bag for spontaneous showers and one for cooler weather. However I had to spray them with waterproof spray as they lost some waterproofing qualities after a few trips in the laundry.
I also dream of a wide-brim helmet for full waterproofing powers!