fix(backend): only warn about a backend switch when the backend kind changes

src/args/backend_arg.rs

@@ -724,7 +724,7 @@ impl BackendArg {
             .first()?
             .to_string();
         let current = self.full_without_opts();
-        (current != registry).then_some((current, registry))
+        (!same_backend_kind(&current, &registry)).then_some((current, registry))
     }
 
     /// [`Self::superseded_backend`], when it is a lock entry that keeps the
@@ -1029,6 +1029,15 @@ impl Hash for BackendArg {
     }
 }
 
+/// Whether two backends use the same backend kind (`aqua`, `vfox`, `asdf`,
+/// `github`, ...), ignoring the repository or package they name. A registry
+/// entry that moves to another repo or org within a kind installs the same way,
+/// so only a change of kind counts as a backend switch.
+pub fn same_backend_kind(a: &str, b: &str) -> bool {
+    a == b
+        || matches!((a.split_once(':'), b.split_once(':')), (Some((a, _)), Some((b, _))) if a == b)
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
@@ -1347,3 +1356,14 @@ fn pypi_and_pipx_use_distinct_tool_identities() {
     assert_eq!(BackendType::guess("pipx:black"), BackendType::Pipx);
     assert_eq!(BackendType::guess("pypi:black"), BackendType::Pipx);
 }
+
+#[test]
+fn same_backend_kind_ignores_the_repository() {
+    assert!(same_backend_kind(
+        "vfox:mise-plugins/vfox-lua",
+        "vfox:jdx/vfox-lua"
+    ));
+    assert!(same_backend_kind("aqua:old/name", "aqua:new/other-name"));
+    assert!(!same_backend_kind("aqua:foo/bar", "github:foo/bar"));
+    assert!(!same_backend_kind("vfox:jdx/vfox-lua", "asdf:jdx/vfox-lua"));
+}

src/args/mod.rs

@@ -1,4 +1,4 @@
-pub use backend_arg::{BackendArg, BackendResolution, split_bracketed_opts};
+pub use backend_arg::{BackendArg, BackendResolution, same_backend_kind, split_bracketed_opts};
 pub use env_var_arg::EnvVarArg;
 pub use tool_arg::{ToolArg, ToolVersionType};
 pub use truncate::TruncateOptions;

src/cli/doctor/mod.rs

@@ -1232,11 +1232,11 @@ impl Doctor {
             };
             // The install state records one backend per tool, so versions installed
             // on either side of a cutover cannot all match it. Only warn when none do.
-            let strip = |full: &str| full.split('[').next().unwrap_or(full).to_string();
-            if recommended
-                .iter()
-                .any(|full| strip(full) == stored_stripped)
-            {
+            // Only a change of backend kind counts; a repo or org rename within one does not.
+            if recommended.iter().any(|full| {
+                let stripped = full.split('[').next().unwrap_or(full);
+                crate::args::same_backend_kind(stripped, stored_stripped)
+            }) {
                 continue;
             }
             let Some(registry_full) = recommended.first() else {