fix(setup): treat empty COPILOT_HOME as unset (#5047)

`copilotDirectory` used nullish coalescing, so `COPILOT_HOME=""` produced
the relative path `mcp-config.json`. Setup then planned and wrote the
GitHub Copilot CLI registration into the current working directory, not
`~/.copilot/mcp-config.json`, and doctor looked for it in the same wrong
place.

Use `||` like the sibling client homes (CODEX_HOME, KIMI_CODE_HOME,
GROK_HOME, XDG_CONFIG_HOME), and as #2686 did for DSH_HOME.

src/application/SupportedClients.ts

@@ -360,7 +360,7 @@ const piAgentDirectory = ({
 };
 
 const copilotDirectory = ({ home, env }: ClientPathContext): string =>
-  env.COPILOT_HOME ?? join(home, ".copilot");
+  env.COPILOT_HOME || join(home, ".copilot");
 
 const commandCodeDirectory = ({ home }: ClientPathContext): string =>
   join(home, ".commandcode");

tests/boundary/cli/clientProfileLifecycle.test.ts

@@ -122,6 +122,12 @@ const cases = [
     config: ".grok/config.toml",
     skill: ".agents/skills",
   },
+  {
+    client: "copilot_cli",
+    env: { COPILOT_HOME: "" },
+    config: ".copilot/mcp-config.json",
+    skill: ".agents/skills",
+  },
   {
     client: "omp",
     env: { PI_CODING_AGENT_DIR: "profile" },