a 12v port on the car is usually 120w or 180w max (it sometimes says) because of the 10-15A circuit breakers and the cables being not thick enough for higher loads. Converting 12v DC to 220v AC to 5v-20v DC for PD3.0 seems highly inefficient, not to mention the waste of space, inverters are not small (if they have any meaningful/usable power rating), they are cumbersome pieces of ****...
Can't you get any decent 12v to PD car charger with 45 or 65W PD 3.0 from a semi reputable Chinese brand: Anker, Aukey, Ugreen, Bitzwolf, etc... ?
EDIT:
e.g.
Aukey Expedition 45W PD Car Charger USB-C
Costs 17 euros which is 15 quid I think.
Remember you need a usb C cable suitable for this as well! Usually a USB C cable rated for 100W (5A at 20v with pd 3.0) should be good enough.
All you need is a charger that genuinely provides 45w with pd3.0 for the Steam Deck.
But anyhow, just buy from a well known brand that actually delivers what it specs...
(USB) chargers are a bit of a **** world, you have the 5V up to 2.4A chargers (the cheaper ones are lucky to do 1A), you have all phone brands ******* about with their own retarded ''fast'' charging protocols E.g. Oneplus, Huawei, Xiaomi (but luckily most accept either QC of PD as well), and then there's both Power Delivery 1.0 through 3.0 and Qualcomm Quickcharge 1 through 3 or even 4. Of course Wireless there's QI as well...
And yeah, many cheap chinese (no name brand) chargers promise PD 3.0 of QC but don't actually support either quick charge protocols or anywhere near their specced wattage, oddly Amazon sells a lot of these as well, I've seen the exact same chargers on Amazon for 20-40 which are litterally 2-3 euros delivered from Aliexpress, but that is to cheap. A general rule is try to find the same things on Ali you see on Amazon (you can use the image search in the app, it works really well). If the price premium is over 200% on amazon then you're just buying dropshipped rubbish. If the prices are similar (amazon a fiver more or so) and realistic for what you het ( e.g. 45w PD 3.0) it should be fine. But you can also google which brands can be relied on for at least their specs.