did governors of states really restrict people from having "elective surgery" and even going to a standard medical clinic? which states? why?

In other countries, they have not been able to balance covid very well.  There are a lot of restrictions on what healthcare treatment is available.

In the US, we have been running our healthcare system at full levels since around May 1, 2020. 

In November/December/January, healthcare systems did reduce "elective surgery" in some areas.  But it was truly "elective surgery" - items that don't make much difference if you do them today versus in a few weeks - like knee replacements.

No. Governors do not have that power.

Hospitals do.

You already selected a "Favorite Answer" but I wanted to add that while "?" is right re the hospitals limiting elective surgery - many urgent (and in my opinion, emergency) surgeries were deemed "elective" = necessary surgery delays.

I was in a bad car accident in June 2020 and had to wait for 14 days before the hospital would allow my surgery to take place (Covid and antibodies testing was only part of the delay). 

It was the hospitals that limited elective surgery, not the government. There were a couple of very good reasons- for one thing, many doctors who normally work in other areas were pulled into the ER and the COVID units because of the overwhelming numbers of patients there. For another, it was risky for anyone to be in a hospital for anything other than COVID treatment- your risk of exposure to the virus was very high. So it was to benefit the other patients that they were advised to wait on elective surgery. No clinics or doctor's office went out of business. However, in some states, the legislature's refusal to accept Medicare expansion money because it came from President Obama DID cause hospitals to close- 11 in my area. That was long before COVID. 

CNN n go go TN h

i think it is still that way in states like CA