Fix TUI app-server permission profile conversions (#16284)

Addresses #16283

Problem: TUI app-server permission approvals could drop filesystem
grants because request and response payloads were round-tripped through
mismatched camelCase and snake_case JSON shapes.
Solution: Replace the lossy JSON round-trips with typed app-server/core
permission conversions so requested and granted permission profiles,
including filesystem paths and scope, are preserved end to end.

codex-rs/tui/src/chatwidget/snapshots/codex_tui__chatwidget__tests__exec_approval_history_decision_aborted_long.snap

@@ -1,5 +1,6 @@
 ---
-source: tui/src/chatwidget/tests.rs
+source: tui/src/chatwidget/tests/exec_flow.rs
+assertion_line: 217
 expression: lines_to_single_string(&aborted_long)
 ---
 ✗ You canceled the request to run echo

codex-rs/tui/src/chatwidget/snapshots/codex_tui__chatwidget__tests__exec_approval_history_decision_aborted_multiline.snap

@@ -1,5 +1,6 @@
 ---
-source: tui/src/chatwidget/tests.rs
+source: tui/src/chatwidget/tests/exec_flow.rs
+assertion_line: 183
 expression: lines_to_single_string(&aborted_multi)
 ---
 ✗ You canceled the request to run echo line1 ...

codex-rs/tui/src/chatwidget/snapshots/codex_tui__chatwidget__tests__exec_approval_history_decision_approved_short.snap

@@ -1,5 +1,6 @@
 ---
-source: tui/src/chatwidget/tests.rs
+source: tui/src/chatwidget/tests/exec_flow.rs
+assertion_line: 47
 expression: lines_to_single_string(&decision)
 ---
 ✔ You approved codex to run echo hello world this time

codex-rs/tui/src/chatwidget/snapshots/codex_tui__chatwidget__tests__exec_approval_modal_exec.snap

@@ -1,5 +1,6 @@
 ---
-source: tui/src/chatwidget/tests.rs
+source: tui/src/chatwidget/tests/exec_flow.rs
+assertion_line: 40
 expression: "format!(\"{buf:?}\")"
 ---
 Buffer {