You’re overthinking it, but please don’t think I’m judging - I’m an overthinker too.
My girls are 4 and almost 6. Nearly every day during toddlerhood they wore the following:
Cotton socks
Cotton leggings, sweatpants or jeans
Sometimes tights
Undies
A vest (an undershirt)
Some sort of top/cardigan/jumper combo
Then for going out-out, they’d wear one of those all-in-one suits, wellies, gloves and a hat.
For just going between the house and the car/pram, etc, a good warm jacket (doesn’t really need to be fully waterproof), wellies or other footwear, hat and gloves (sometimes).
In the summer, much the same but sometimes you can get away with no jacket and for like three days of the year, you can wear summer clothes.
The thing about the rain here is that while it falls frequently, it’s not heavy, soaking rain like in the states. It CAN be soaking, but mostly it’s just mizzle. The rain gear is mostly because all the surfaces are wet.
Might be worth bringing wellies and a jacket just so you can tell them apart from everyone else’s same exact jacket and wellies purchased from Lidl/ASDA/etc.