perf(nushell): cache static prompt context

- precompute os symbol, user/host, ssh flag, shell label and newline sequence at startup

- reuse cached values in _pj_left_prompt to reduce per-render overhead

nushell/modules/pj_prompt.nu

@@ -548,9 +548,7 @@ def _pj_lang_segments [] {
     $out
 }
 
-def _pj_left_prompt [] {
+def _pj_prompt_static_base [] {
-    let p = ($env.PJ_PROMPT_PALETTE? | default (_pj_palette_default))
-
     let user = (try { whoami } catch { "" } | into string | str trim)
     let effective_user = if ($user != "") {
         $user
@@ -560,16 +558,31 @@ def _pj_left_prompt [] {
 
     let host = (sys host | get hostname? | default "")
     let in_ssh = (($env.SSH_CONNECTION? | default "") != "" or ($env.SSH_TTY? | default "") != "")
+    let prompt_newline = if (($nu.os-info.name | str downcase) == "windows") { "\n\r" } else { "\n" }
 
-    let user_color = if ($effective_user == "root") { $p.c_root } else { $p.c_user }
+    {
+        os_symbol: (_pj_os_symbol)
+        effective_user: $effective_user
+        host: $host
+        in_ssh: $in_ssh
+        shell_name: "nu"
+        prompt_newline: $prompt_newline
+    }
+}
 
-    let host_part = if $in_ssh {
+def _pj_left_prompt [] {
-        $"($p.c_host)@($host)($p.c_reset)($p.c_ssh)  󰬚󰬚󰬏 ($p.c_reset)"
+    let p = ($env.PJ_PROMPT_PALETTE? | default (_pj_palette_default))
+    let static = ($env.PJ_PROMPT_STATIC? | default (_pj_prompt_static_base))
+
+    let user_color = if ($static.effective_user == "root") { $p.c_root } else { $p.c_user }
+
+    let host_part = if $static.in_ssh {
+        $"($p.c_host)@($static.host)($p.c_reset)($p.c_ssh)  󰬚󰬚󰬏 ($p.c_reset)"
     } else {
         ""
     }
 
-    let shell_part = $"($p.c_shell) nu ($p.c_reset)"
+    let shell_part = $"($p.c_shell) ($static.shell_name) ($p.c_reset)"
     let dir = (_pj_truncate_pwd $env.PWD 4)
     let git_part = (_pj_git_branch_module $p)
 
@@ -596,8 +609,8 @@ def _pj_left_prompt [] {
     let duration_part = $"($p.c_duration) 󱫑 ($duration_text) ($p.c_reset)"
 
     mut out = ""
-    $out = $"($out)($p.c_os)(_pj_os_symbol)($p.c_reset)"
+    $out = $"($out)($p.c_os)($static.os_symbol)($p.c_reset)"
-    $out = $"($out)($user_color)($effective_user)($p.c_reset)"
+    $out = $"($out)($user_color)($static.effective_user)($p.c_reset)"
     if ($host_part != "") { $out = $"($out)($host_part)" }
     $out = $"($out)($shell_part)"
     $out = $"($out)($p.c_dir) ($dir) ($p.c_reset)"
@@ -605,8 +618,7 @@ def _pj_left_prompt [] {
     for m in $lang_parts {
         $out = $"($out)($m)"
     }
-    let prompt_newline = if (($nu.os-info.name | str downcase) == "windows") { "\n\r" } else { "\n" }
+    $out = $"($static.prompt_newline)($out)($time_part)($duration_part)($static.prompt_newline)"
-    $out = $"($prompt_newline)($out)($time_part)($duration_part)($prompt_newline)"
     $out
 }
 
@@ -623,6 +635,7 @@ export-env {
     load-env {
         PJ_PROMPT_PALETTE: (_pj_palette_default)
         PJ_OS_KEY: (_pj_detect_os_key)
+        PJ_PROMPT_STATIC: (_pj_prompt_static_base)
         PROMPT_MULTILINE_INDICATOR: ":"
         PROMPT_INDICATOR: {||
             _pj_prompt_indicator