windows: Fix inconsistent separators in buffer headers and breadcrumbs (#38898)

Make `resolve_full_path` use the appropriate separators, and return a
`String`.

As part of fixing the fallout from that type change, this also fixes a
bunch of places in the agent code that were using `std::path::Path`
operations on paths that could be non-local, by changing them to operate
instead on strings and use the project's `PathStyle`.

This clears the way a bit for making `full_path` also return a string
instead of a `PathBuf`, but I've left that for a follow-up.

Release Notes:

- N/A

crates/util/src/paths.rs

@@ -280,6 +280,17 @@ impl PathStyle {
             ))
         }
     }
+
+    pub fn split(self, path_like: &str) -> (Option<&str>, &str) {
+        let Some(pos) = path_like.rfind(self.separator()) else {
+            return (None, path_like);
+        };
+        let filename_start = pos + self.separator().len();
+        (
+            Some(&path_like[..filename_start]),
+            &path_like[filename_start..],
+        )
+    }
 }
 
 #[derive(Debug, Clone)]