refactor(doctor): show detected LSP servers and extensions instead of hardcoded counts

Replace the hardcoded 4-server list in doctor LSP check with getAllServers()
from server-resolution.ts, which covers all 40+ builtin servers plus user
config. Output now shows server count with supported extensions, and verbose
mode expands to per-server detail lines.

Status:  LSP 3 servers (.go, .py, .pyi, .ts, .tsx)
Verbose: LSP 3 servers (.go, .py, .pyi, .ts, .tsx)
           typescript (.ts, .tsx, .js, .jsx)
           pyright (.py, .pyi)
           gopls (.go)

Closes #2587

src/cli/doctor/formatter.test.ts

@@ -19,8 +19,10 @@ function createDoctorResult(): DoctorResult {
       isLocalDev: false,
     },
     tools: {
-      lspInstalled: 2,
-      lspTotal: 4,
+      lspServers: [
+        { id: "typescript", extensions: [".ts", ".tsx", ".js", ".jsx"] },
+        { id: "pyright", extensions: [".py", ".pyi"] },
+      ],
       astGrepCli: true,
       astGrepNapi: false,
       commentChecker: true,
@@ -102,7 +104,7 @@ describe("formatDoctorOutput", () => {
       const output = stripAnsi(formatDoctorOutput(result, "status"))
 
       //#then
-      expect(output).toContain("LSP 2/4")
+      expect(output).toContain("LSP")
       expect(output).toContain("context7")
     })
   })