When a website is remodeled, are the URLs of the posts and pages kept? Is the positioning maintained?
In most cases, you would want to keep the URLs of the posts and pages the same. If the pages had good organic rankings, maintaining the URLs is essential to maintaining those rankings. Additionally, if URLs are changed, and proper redirects are not in place, users will experience errors, and your site risks losing rank. Whether or not you change positioning is entirely up to you. With every website update looking at content and whether it brings value to visitors is critically important.
I highly recommend implementing 301 redirects if you are changing your URL structure. This will help preserve some of the positive SEO signals you have generated. Keep the URLs as is if solely the content is changing. Typically preserving URLs is the recommended approach.
Positioning and messaging are separate from the technical implementation of the URLs. Any time you change your copy, even if for positioning, the content is different therefore your SEO rankings may change.
Focus on delivering helpful and valuable content not content solely for SEO purposes.