In terms of your connection, LAN and WAN isn't really going to be the way to go except for some very specific scenarios.
The Steam Deck and almost all multiplayer games connect via Internet servers and your steam accounts. Some games you can host and your friend connects directly via the Internet - games are designed to support that so you often don't need to resort to local LAN/WiFi play.
It doesn't matter that you're next door to each other - you might as well be miles away from each other for all it matters - you both just need good stable internet connections to the remote servers, with decent speed and your Internet routers not too restrictive on your connections (firewalls not blocking access, relevant ports open).
So basically ensure you have a good WiFi connection. Even better you can also get USB c ethernet dongles or a dock for your steam deck with ethernet to connect to your router directly and avoid WiFi.
I play with my steam deck docked under the TV, ethernet connection to my router, hdmi to my TV and an xbox controller and Bluetooth headphones. I play on the couch with all the benefits of the steam deck.
Both of you docking your steam decks with ethernet connections to your Internet routers may give you a better experience.
Edit: In terms of games to try:
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Phasmophobia - you can cooperatively try and hunt ghosts, horror game but can be a lot of fun
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Keep talking and nobody explodes - coop game where you diffuse a bomb, hectic but not needing fps reactions
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Divinity: Original Sin 1 & 2 - RPG games which can be played in Co op mode, with tactical combat
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Baldurs Gate 3 - similar to above, same makers but hugely popular and highly regarded game
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Valheim - coop survival game - explore and build a base, defeats bosses etc
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Stardew Valley - super cosy farming sim, with simple combat. It's a very chill multiplayer experience - can just chat away (or not) while building up your joint farm
There are loads of co-op type games that work well on the Steam Deck.
Lots of good advice but one question - have you tried LED bulbs before and had flickering problems?
Just worth checking a standard LED from your local super market before you go down the route of expensive brands or online purchases.
The reason I say this is that there are a lot of shoddy cheap and counterfeit electronics sold on Amazon for example. A supermarket bought bulb meanwhile actually has some quality control and standards plus you have somewhere you can go back to should you need to return them.
All my LEDs are from my local supermarket, own brand (Tesco, I'm in the UK, but Philips are also available for me) and I've had no issues. I'd also buy from local retailers where you can get good returns policies (Argos here, or your big box retailers in the US)
Amazon meanwhile has a policy of mixing stock that it purchases with stock from small sellers that they place in their warehouses and sending any to a customer. So a "sold by amazon" item may actually be a counterfeit item supplied by a 3rd party. Basically do not buy anything of value or branded from Amazon. So don't buy Phillips or other brands from Amazon.
And definitely do not buy the cheap Chinese unknown brands on amaxpn or elsewhere. The supermarkets will of course be buying Chinese made bulbs for their own labels but they will be buying them in bulk from specific factories and under contracts with some quality expectations, unlike the shitty free for all small seller type sourcing that your get from Amazon. Small sellers are going to be buying cheap ass unbranded bulbs and the factories are going to sell their cheapest bulbs plus ones that's do not meet bulk orders quality control thresholds via this route (cheaper to dump the bulbs by selling cheaply instead of having taking the financial hit and binning them). A large supermarket has leverage over the factories to maintain quality (or lose the contract) while small sellers have none.
Personally the only time I had a flickering LED bulb was a dimmer-switch lamp; it was designed for LEDs but didn't work with the bulb I bought but turned out I'd accidentally bought a non dimmable bulb. Otherwise I've not had a single bulb flicker in my house including all ceiling lights and numerous lamps. All my bulbs are supermarket own brand.