As far as new rifles for it, extinct. There are however many rifles still around, and most are in good condition. I bought a 700 classic in 350 RM about a year ago. The latest offerings came with a faster twist, like 1:12. I believe Rugers were 1:14. Original twist was 1:16. The Remington's have a 2.800" magazine, that's it, not any longer. The Ruger magazine is longer, probably just under 3.00" as I've seen OAL listed at 2.96" app.
What this means is that not all 350's are the same. Some are intended for heavier bullets, some for lighter ones, 250gr vs 200gr. My 700 Classic has a 1:16 twist and a 2.800 magazine, I settled on a load with 200's. I use a Hornady FTX and get good accuracy @ 2800 fps. I've used CFE 223 and Varget. Realistically, it is best suited for whitetail loaded this way. My rifle is 42" long and light enough to carry and almost heavy enough to tame the recoil somewhat. Interestingly it is the same length as my 336 in 35 Remington. I load the same bullet in it, at about 2000fps.
35 (and 9mm) cal. rifles are odd ducks, have a following but never been that popular. As far as readily available ammunition the Whelen and 35 Rem are it. The 35 Whelen has some of the same issues as the 350, available in both slow and fast twist. With a 16 twist it is best with 200gr bullets, with 12 twist 250's are best. The 350 Rigby was bested by the 375 H&H, although there was nothing wrong with the 350 Rigby. Starting at 35, rifles have the advantage of caliber, it seems to be the point at which the diameter of the bullet starts to become an advantage. There are lots of articles and such on the 35's, they serve a purpose.
I consider my 350 with 200's an express loading, a light for caliber bullet at "higher" velocity. IMO, the Ruger is the ideal platform for the 350, with it's longer magazine, faster twist, and 3 position safety.
My 336, 35 Rem is my bushwhacker. The 200 RN Core-Lokt is a good load, but hard to find on the shelves here, so I load the 200 FTX, they are just as accurate.