Iirc they made literally no money or even lost a bunch on base models, and only the higher range models made any "profit". But they now sell the "base model"with better specs at the same price today, so I'm confident their prices will be reasonable.
The reason og steam machine failed was they were relying on so many other companies, and didn't have a good framework yet, but steam deck was an immense success, so I see literally no reason this can't succeed.
The reason any of this exists is because Microsoft was threatening to force all software come from the Windows Store when Windows 8 was about to release. Valve realized that it'd kill Steam, so they wanted to make Linux work as a gaming platform. Even when Microsoft walked it back, it's not safe for Valve to be dependent on the whims of Microsoft.
The main problem with original steam machines was that they came out before Proton was good: the goal was to get companies to put out native Linux versions. That's essentially how consoles work: you put out a console, and force video games to be written for / ported to your console's OS. But with consoles, you put out hardware for cheaper than it costs to manufacture, and make up the money on the video game sales. Valve had third parties putting out the Machines, so the third parties had to get profit on the sale of the machine. At that point, it was just a prebuilt PC without Windows, which locked you out of playing 90% of games. If you were in the market for a Steam Machine, you could just buy a prebuilt windows machine for the same price and play every PC game. So no one had any reason to buy a Steam Machine, and developers didn't have a reason to port to Steam Machine (Linux).
So they spent years of R&D to make proton work well enough to run 90% of games, and put out Steam Deck at a loss in a niche market where there was really no competition and where Windows is impractical. So now, a Steam Deck still can't play every game (due to anti-cheat), but there's still reasons to buy it.
Do you already have a Steam library, but want something portable like a switch? Deck lets you play 90% of your games you already own, switch requires you to buy all new. The Steam deck library, despite missing 10% of games, still had a much larger library than a switch, with much more powerful hardware, and was cheaper once you figure in the switch game pricing (assuming you count the games you already own). You could even play the unsupported games on it via streaming from your existing rig. I think this is the market they were trying to capture. Now Steam Deck / Linux has a big enough market share where if a game isn't supported, there's a reason to try to fix it. Today, basically every game works with the exception of specific forms of anti-cheat.
Do you currently not have a steam library, but want to play some PC exclusive stuff? Steam deck was the cheapest way to do it, $/performance, because it was sold at a loss. Even if you plugged it in to a TV permanently it was more cost efficient than buying a PC, because graphics cards had insane costs at the time. I don't think Valve was planning for this market, but it turns out it's bigger than they anticipated.
I presume that that's the intent of the new Steam Machine: It's just a steam deck where they took out the screen and used that money to make the hardware more powerful. Sort of the opposite of a Switch Lite. I think it's also to test the waters for the next iteration, they're not out much if this flops.
With the VR headset they're doing kind of a similar thing as with the Deck, where the goal is to get everything to run on ARM. Today, if you buy a VR headset and your favorite game doesn't run on it, that's fine, because most people buying a new VR headset have a rig already and they can just stream it (like every other VR headset). But they'll still get bug reports for stuff that doesn't work on ARM, and they can fix it in the compatibility layer. If they can get basically everything to run on ARM, they'll eventually be able to put out gaming PCs / Steam Machines at a lower cost than the equivalent Windows machine, and once that happens there'll be very little reason to buy a Windows PC for your gaming rig. Then they can go back to the original Steam Machine model where they let other companies build the machines: The other companies can undercut the Windows machines while still turning a profit, and they're forced to use Linux/SteamOS because Microsoft can't figure out ARM.