Medically undiagnosed condition: how to inform?

I think you should inform your thesis comittee about your current situation. Best case, they are understanding, worst case they will ignore it for PhD-related matters. It might help to get a sick note from an independent professional even if the diagnosis is difficult.

As to your second question, I would suggest to not disclose any health issues in the hiring process for the same reasons as stated in your linked questions, unless the position is specifically advertised as 'disabled applicants preferred' which I believe is a thing in Germany, for example.

Regarding your third question, I cannot say in general whether discrimination is to be expected. Depending on your condition and country of future employment, there may however be laws in place to protect you from discrimination against your condition. I can only offer limited advice on how to deal with discrimination otherwise, but coping strategies against pain may be of interest to you in case of chronic problems, and may be subsidized by (potentially employer-paid) health care.

I think that the fact that you don't have a diagnosis is not unusual. Pain is, if I've read correctly, poorly understood by the medical community. This has led to over prescribing of opiates, for example.

For your committee, just tell them. I doubt they would change their supportive attitudes now.

For the long term, there may be no real effect on your productivity if you can obtain some assistance in certain tasks. There are other 'disabled' academics who do well using students and other associates to help manage impossible tasks. The blind and deaf, for example. Stephen Hawking comes immediately to mind, of course.

As for the issue of informing employers it might depend on location. I have no specific knowledge about UK/EU or other places such as India, but in the US it would likely be regarded as improper to consider it as a condition of employment but, on the other hand, might give notice that you will need assistance for some tasks. As for the lack of diagnosis, if you want to inform a potential employer, a letter from one of your physicians explaining the situation is probably best.

And, of course, don't take diagnosis suggestions from a place like this. Your condition may be long term or not. But even if it is long term, you can find ways to compensate and be productive, though the pain won't be less.