Layers are the way to go. You can use the same rain jacket year round as your shell.

For the jacket get a good (NOT just DWR) rain jacket (I use a Helly Hansen 2.5 jacket). Helly Hansen, Outdoor Research, Patagonia, etc are all good options. Sailing companies typically make good stuff, pay attention to the millimeter waterproof rating. The 2.5 layer fabric is a nice blend of breathability, packability, and waterproofness imo since I don't want to be sweating inside the jacket. If you happen to work as a first responder, outdoor professional, military, etc most of these high end outdoor gear companies have a "pro" program you can register for and receive 50% off your purchases.

Underneath that, as it gets colder layer whatever you already own for an insulation layer (polyfill puffer, wool sweater, stanfields, etc), I would avoid down fill in this case just in case you do ever soak through your jacket since it will lose its insulation capacity when wet.

For shoes I don't really have a good recommendation since I just use waterproof socks and wear whatever shoes I feel like.

I would also definitely second using a standalone rain jacket. Even the best rain jackets are going to end up holding some humidity in depending on how hard you bike, so you want to be able to go without a rain jacket when you can.

When you aren't wearing the rain jacket, you want to be wearing something that acts as a decent windbreaker. The warmest sweaters don't work too well when you are on a bike moving fast. Puffy jackets are nice cause they pack down small, and generally block wind well. Like mentioned above, down doesn't work as well when wet, and synthetic fill is cheaper anyway. You can get a puffy jacket used to save some money. I'm not too convinced that one brand's synthetic filling is better than another's, just get something with a decent amount of filling, and wash the jacket according to the instructions to help fluff it up.

For an actual waterproof layer, I wouldn't try to get used, unless it looks in really good shape. When the membrane on the inside of the jacket starts to break down, there's nothing you can do. Just get something preferably 2.5 or 3 layer. Look in my comment history for an explanation of what that means. Armpit zippers are going to be really important. I'm not sure what brands are available to you, but try to find a brand that's been around for a while that's not really trendy. Patagonia makes good stuff, but it is expensive, and you can get a jacket made from materials that are just as good for 1/3rd of the price. Quickly googling European brands that might work, I found there's eu standard 343:2019 that rates the waterproofness of work clothing. Something with a 4/4 rating looks like it would be good. I was just looking at engelbert Strauss. No clue if they are actually a reputable brand, but seems cheap and effective.

For shoes, it's a bit harder. I just wore boots when I had to bike in winter, but I think using gaiters is probably the best way now. That way you could wear whatever shoes you like, but keep water and wind out. It's nice to keep any road grime off of your shoes and lower pants.

I know I'm late to this but I figured I'd give my experience incase it helps someone else who finds it. I'm a big fan of cycling capes. I've got a clever hood and a carradice. They keep the rain off while preventing overheating. I find my legs get wet so I wear rain gaiters or tall rubber boots

I tend to prefer the carradice due to how stiff and quiet the fabric is.

Underneath, I wear the same cold weather gear I would wear normally. A warm wool sweater is usually plenty unless it's really cold in which case I'll wear an unzipped windbreaker over the seater

In case you didn't find anything and now that the cold spring showers are starting, check multiple second hand stores for a leather jacket with a wool lining, and look separately for a rain proof bike helmet. You can also get plastic safety glasses of you want as well for only like 2 euros more. I had the same issue as you of over heating in a rain jacket. You should find all that for Uber 100€>