It depends.
My experience is that emergencies are handled quickly. Routine things can take quite some time. Urgent but not emergency, all over the ball park.
Much depends where you live. Urban areas are better served with health care providers so one likely can get seen sooner than in exurban or rural areas where there are fewer providers.
So with that said, here are my experiences in the Höfe area, where, based on your other threads, you might end up.
Be aware that there is a shortage of GPs who are taking new patients. Get on the books with anyone you can, even if you have to go a bit farther afield, then later start looking for someone who best meets your individual criteria.
FYI, I was told that closing the practice to new patients is one way that GPs are trying to provide care in a timely manner.
To see my GP, who only works part time (which is becoming more common among GPs these days), the worst wait was 6 weeks. On the other hand, I have been able to get a same day appointment in an urgent situation. My typical wait to see the GP is two weeks.
I go to a group practice which has some of the 'bells and whistles' in house - but the things you list are generally provided by specialist practices in this area.
There are private imaging centers in Pfäffikon SZ and in Einsiedeln where MRIs are done. (Einsiedeln hospital does not have MRI capability, not sure about Lachen or Schwyz.) You would need a GP referral, but once you have that my experience has been that appointments at both imaging centers can be made quickly, usually within a week.
A routine screening colonoscopy is likely a 4-6 months wait. Again, seeing a gastroenterologist usually requires a GP referral.
An urgent colonoscopy/gastroendoscopy can be done at either local hospital, wait times will depend on the degree of urgency. There are also a couple of private Gastro practices.
I am currently waiting for a 'semi-urgent' appointment. I had decided to have it done out here because I don't fancy trekking into Zürich Unispital right now. It was recommended that I have it done within 'a few weeks' but it's now been six weeks, still waiting for the appointment letter from the gastroenterologist. I don't know if the delay is due to the specialist's schedule or because my GP has not yet done the paperwork.
Speaking of Unispital, where more complicated things are referred, my experience wiht outpatient consultations: After being referred by the GP, I waited one month to receive the appointment letter from the hospital, another month for the appointment itself, a third month for the report to get back to my GP. Again, urgent but not emergency.
BC, or any visit to the gynecologist: Here is where the shortage is evident. Again, go with any gynecologist who has open books. A female gynecologist who is willing to consult in English and is open to new patients can be tough to find. Routine gyne appointments, non pregnancy related, take 4-6 months; typically I make next year's screening appointment when I am leaving this year's.
Pregnancy related appointment are altogether different and take priority. You can generally be seen quickly.
Non-routine urgent apppointments are generally available quickly, although your gynecologist might send you to the hospital instead due to availability.
Knee surgery... no idea. Be aware that kee surgery, and others typically done outpatient elsewhere are more often done inpatient here. A friend recently had knee surgery done - 3 days in the hospital followed by 10 days in a rehab clinic.
This however likely is changing as costs rise, there is more and more discussion of surgeries now done inpatient moving to outpatient.
Although everyone likes to think differently, I have seen private insurance make a difference in the speed with which you get a specialist appointment. I once got an appointment unexpectedly quickly - only to be called back and told that there was a mix-up, given that I only have basic insurance the wait would be longer. Only one anecdote, make of that what you will.
I only have basic insurance because I had a prexisting condition when we moved here, I didn't qualify for supplemental insurance. If you qualify I would strongly recommend getting it.
As with everything in Switzerland, YMMV.