Is there a website that lists a ton of wheels and lets me filter based on stuff like tubeless compatible, material etc.
Full carbon clincher, rim brake, tubeless, 50mm deep. Does that exist
Or is carbon rim braking and tubeless hard to achieve. I see Prime (i think they are Chain Reactions own brand) have it. Looking at the big wheel guys, Zipp+Mavic neither seem to. Zipp have tubeless support on their 303 disc brake version.
I don't think there's a website to list every wheel & their specifications as you listed above.
Fulcrum & Shimano do a range of wheels, from aluminium, carbon/alu, full carbon, clincher, tubeless (or both), various depths etc.
I run Fulcrum Racing Zero, tubeless of course. Can't fault them, brilliant climbing wheels, no good for a TT though or other flat races
Prime seem good value for money, I toyed with them for my winter bike, but Shimano RS610 are probably the better option in that kinda price range, or the Ultegra wheelset if you have another £75 spare.
DT Swiss also do a good range of wheels and I'm pretty sure most are tubeless compatible and have disc options too. I used to have a set of DT Swiss RR1450's, very light, tubeless but did flex slightly under power on climbs.
Unfortunately though you'll just have to research and hunt around to find something that suits your requirements, IE: Climbers wheel, TT wheel, general purpose, tubeless etc Just remember if you buy a proper carbon wheel, with a carbon brake track, you need carbon pads. (Unless its disc).
You can convert most (perhaps all) wheels to tubeless with a variety of kits.