Rav Asher Weiss gave a whole shiur on the general subject of inadvertent killing someone after a bachur wrote asking what teshuva he had to do after infecting people who died. He brought down Rabbi Akiva Eiger’s teshuva (Mahadura Tanina 3) regarding someone who caused a wagon accident in which two people were killed. Among the things the person had to do was fasting every Mon and Thurs for a year, not to any simcha other than his children’s weddings, send an orphan to yeshiva until age 19, and then send another until age 18, and establish a kollel where the avereichim will learn for illuy neshmot the niftarim and say kaddish.
Getting the jab is no big deal unless you have a specific medical issue. If you have recovered you might only need one. I am shocked that people who are machmir on any little minhag are so meikal on nefashot.