Shipping never took months. What took months was the time until you were allowed to order.
There’s no such thing with the OLED (at least not until now), so everyone who already ordered one should get it in the time frame Valve mentioned - 3-5 business days for the early buyers, 5-10 business days for the later buyers.
Refurbished LCD 512GB is still in stock in Europe at the moment.
Why are they selling it?
Probably because they bought an OLED Deck and are trying to get some money from their LCD one before the market is flooded with LCD Decks.
You don’t need a router, you need an Access Point.
So, either a standalone Access Point, or a router with WiFi where you can disable the router part in the settings.
Then, if you just use the same WiFi name and password it should look like one big WiFi to all devices.
And if you have a hardwired ethernet cable, of course you use that instead of Powerline, it’s going to be way faster and way more stable.
You don’t need a dock to plug in devices like controllers or keyboards or ethernet adapters into the Steam Deck. You’d only need that for high-power items which a keyboard is certainly not.