Here's the misinformation or the misunderstanding of the difference between all of those vaccines and the COVID stuff.
The list you pointed to gives FULL IMMUNITY against the disease. In other words you will not get sick.
Thats clearly not the case with the COVID stuff. The COVID vaccines don't give full immunity, just a better shot at survival and bad cases, less potential spread too. Thats been acknowledged by public health, the politicians and the manufacturers.
When someone authorizes a vaccine as good as the ones in your list, then COVID doesn't belong in that list.
Here's the deal with chicken pox (Varicella).
https://www.cdc.gov/vaccines/vpd-vac/varicella/hcp-effective-duration.htm