Note, in this discussion, I'm talking about about the "radar unit" or "radar module" which includes all the components that you talk about above. I only refer it to "radar" as it's redundant to add "unit" or "module" to it. I see no evidence of "radar unit" or "radar module" shortages.
What Elon mentioned about writing firmware for replacement microcontrollers would not be applicable to the radar situation given they aren't replacing the microcontrollers inside the radar module (it's sold as a whole unit, so it's not like Continental would ship them ones without the chips), rather they are removing the whole radar module from the car (no replacement). So Elon is obviously talking about some other part in his comments.
I see however evidence of shortages of various control modules, infotainment and navigation systems, ADAS control modules (like ESP control modules, Mercedes Pre-safe). That's what I'm talking about.
OK, understood, but part of what I wrote is that controllers are also in the radar units, not necessarily separated into a controller module. To focus on controllers (aka MCUs, basically processors + some hardware I/O):
I searched just a little - here is a rather long article that mentions radar albeit in passing, in the context that nearly everything in the car uses MCUs, including ADAS features. The quote is emphasizing that the shortage is everything, not just increased ADAS content - but yes including that. And I think it's a safe bet that the radar module itself includes catalog-MCU or integrated custom-MCUs.
"But most of what we’re seeing the constraints in right now is MCUs, and that’s a lot of the legacy automotive stuff. It’s engine controls, transmission controls, steering, airbags, radios. It does touch some of the ADAS stuff — radars, front-view cameras. But the reason we’re having this problem is because the MCUs are literally everywhere in the car. It’s not like I’m just going to order a car and I’ll take some of the more modern features off, and then I’ll be able to get it. No, if you want the car to run, it’s got to have several microcontrollers in it. So it’s not the case that ADAS is the thing that’s causing this. It’s really the trend of putting more electronics in cars.”
Automotive IC Shortage Drags On
I would add that there are plenty of articles about RF semiconductor shortages also, as a whole post-Covid surge of 5G cellphones and infrastructure is ramping. This very probably affects the radar RF signal chain as well.
It's also easy to find articles about particularly bad delinquency / cost / profit problems at Continental, though they make many other things besides radars. The gist is that Continental did a particularly poor job of managing the supply disruption. If you negotiated particularly aggressive pricing and JIT terms based on your volume, but then you panic in a downturn and break the contract by refusing delivery, don't be surprised that your supplier doesn't put you right back to the front of the line in the upturn. This kind of thing happened across the auto industry, but Continental is apparently a prime example.
So I think we agree that as outsiders we don't have exact knowledge, and again I'm not arguing with you about what exactly is the supply situation and how it feeds Tesla's actions. But a lot of signs point to the conclusion that this is a likely factor. I posted that it made sense given the BMW radar story.
Like you, I also wouldn't tie this directly to Elon's comments about control-firmware rewrites. But it's reasonable to conclude there is an assortment of problems, some buried in assemblies that Tesla has no direct ability to fix. And I guess, if you stretch the interpretation, perhaps he could have been including the big AP rewrite in his explanation, thus obviating radar and thus obviating its need for an associated missing MCU. But I don't actually subscribe to that - it's like deep Biblical or Talmudic analysis over some comments that Elon, not a deity, made to get through a meeting with some analysts, a meeting that he wanted to be over so he could go back to doing something interesting.