Well, most all LLMs appear to function on highschool-level American grammar rules. Given you started sentences with And and But, I safely presume you are not an LLM.
Claude often starts a sentence with 'But'. (There are several examples in my recent conversations, which I checked in case I was misremembering.) 'And' seems to be much less common, but it would use that too if instructed to do so as a humanising trick.