Welcome to the forum and hopefully to Switzerland soon.
From what I can see with a bit of googling it is available here. Any resident in Switzerland, not just citizens, must have at least basic health insurance cover from a recognised Swiss health insurance company. Pre-existing conditions must be covered under the basic health insurance so yes, costs would be mostly covered.
I say mostly because the Swiss system works like this. When you choose your medical cover you choose a franchise. This can be from 300 to 2,500 francs. This franchise is what you have to pay out of your own pocket before the health insurance kicks in to pay medical costs. So in your case it would be best to choose a low franchise - 300 or 500. This means your premiums will be a bit higher than someone who chooses a 2,500 franchise.
Once your franchise is used up there is then another part of the equation - the part-quote it’s called in French. Basically it means you pay 10% of the next 7,000 francs of medical costs while the insurance company pays the remaining 90%. If/when you get past that point then the insurance company picks up the whole tab.
All of this resets at the start of a new year so you’d be back to paying the franchise, then the part-quote from January.
Obviously if someone is healthy the higher franchise for lower premiums is the way to go, but it’s not worth it in your case.
As an example we have a 500 franchise and my husband needs expensive medication that costs just under 4,000 francs for a 3 month supply. So effectively for a large part of the year he pays nothing since he’s used up both his franchise and his part-quote.
You can use this site to play around with figures and look at the various options for health insurance plans.
https://en.comparis.ch/krankenkassen/default
Supplemental insurance is things like a private room in a hospital if you need to go to one, dental cover, etc. If you need special treatments for your Crohn’s then you may need to see if it falls under supplemental because it may not be covered by the insurance companies here since they can refuse supplemental coverage, unlike the basic which they must give you.
If you do decide to accept the job offer then get a prescription for the medication from your doctor to bring with you and make sure it has their contact details just in case your new doctor here wants to contact them. Also bring any medical records you can get hold of.