I think a proper answer to this question would involve a detailed outline of Hexbear’s entire threat model. Would be a more appropriate briefing to get for the folks doing devops in an encrypted matrix chat, not just a post.

Could the government of that country take Hexbear down, if so it pleases?

There are likely several jurisdictions that could take down any given website. I don’t think we’re in the realm of running nested VM’s, proxies, and ever-changing URLs to make censorship more difficult. It’s probably just running on a rack mount somewhere.