Remember there are two distinct kind of Latin pronunciation. The one you’ve been discussing is Medeival, or ‘Church’ Latin. pronounced rather like Italian. The older is Classical Latin, as used by politicians at the end of the Republic. It that kind of Latin Caesar is pronounced much like ‘Kaisar’ in German, hard ‘C’. Medeival Latin pronounces Caesar as in ‘Caesare Borgia’, with a ‘ch’ sound for ‘c’. I do not know where the English soft ‘c’ as in Julius Caesar came from.
Actually, I almost flunked Latin in High School,lol!