For comparison, commercial tools like Confluence support this behavior in several ways. You can copy "friendly" links (which are based on the page title) OR "static" links (which are based on UIDs) directly from a sharing menu item on each page. In addition, if someone tries to use a "friendly" link to access a page that has since been moved, Confluence will trigger an automatic redirect to the new location for that page. The redirect is smart enough to track changes in relative paths / namespaces as well as page renames. The only "caveat" it has is that the redirect only works so long as another new page with the same name/title hasn't been created in the same location since the original page was moved, which I think is a reasonable concession in most cases.

One point to clarify here which doesn't seem to be stated explicitly is that moving wiki pages may also break incoming links from external sources, so simply updating existing page references elsewhere within the same wiki is not sufficient to properly address this problem imo.

However, so long as as page IDs remain consistent / static when pages gets moved or renamed, then using IDs in shareable links could be a suitable alternative to the problem. So long as the IDs / static links are easily accessed somehow from the web UI (ie: "hacking" the URL with various markers to try and extract the internal IDs from them is definitely not "user friendly")