I don't think Picard's statements are continuity errors. They actually reflect what he
wants Starfleet to be, not necessarily what it is
Given that Picard also has an interest in archaeology, he's clearly interested in learning about the universe. He explores the past via archaeology and the present via a starship. He doesn't see himself as a soldier or a warrior, but that doesn't mean he's representative of the whole of Starfleet.
I imagine that most of Picard's career was spent exploring. He graduated in the late 2320s, but the first conflicts that we've heard of in that era were in the 2350s, the Cardassian border wars, in which he was at least briefly involved. So for most of his career he was occupied with exploring rather than fighting. That would leave a lasting impression on him, leading him to think of Starfleet as an exploratory organization.