tui: recover local state db startup failures (#22734)

## Why

#22580 made app-server startup fail when the local SQLite state database
cannot be initialized. Embedded/local TUI startup still continued on the
permissive path, which left the CLI inconsistent and could hide a real
startup problem behind unrelated UI. This brings local TUI startup onto
the same fail-closed behavior while keeping recovery humane for the two
failure modes we are seeing in practice: damaged database files and
startup stalls caused by another process holding the database write
lock.

## What changed

- Embedded TUI startup now uses `state_db::try_init(...)` and returns a
typed `LocalStateDbStartupError` that preserves the affected database
path plus the underlying failure detail.
- CLI startup handles that failure before entering the interactive TUI:
- lock-contention failures tell users to quit other Codex processes and
try again
- failures consistent with a broken local database offer a safe repair
that backs up Codex-owned SQLite files, rebuilds local database files,
and retries startup once
- declined or unsuccessful repairs print concise guidance plus technical
details
- Shared startup error plumbing lives in `tui/src/startup_error.rs`,
while CLI recovery policy and focused recovery tests live in
`cli/src/state_db_recovery.rs`.

## Verification

- `cargo test -p codex-tui
embedded_state_db_failure_is_typed_for_cli_recovery`
- `cargo test -p codex-cli state_db_recovery`
- Manually held an exclusive SQLite lock on `state_5.sqlite` and
confirmed the CLI shows lock-specific guidance without offering repair.
- Manually exercised the repair path with a deliberately invalid
`sqlite_home` and confirmed it backs up the blocking path and resumes
startup.

codex-rs/tui/src/cli.rs

@@ -5,7 +5,7 @@ use codex_utils_cli::ApprovalModeCliArg;
 use codex_utils_cli::CliConfigOverrides;
 use codex_utils_cli::SharedCliOptions;
 
-#[derive(Parser, Debug)]
+#[derive(Parser, Clone, Debug)]
 #[command(version)]
 pub struct Cli {
     /// Optional user prompt to start the session.
@@ -89,7 +89,7 @@ impl std::ops::DerefMut for Cli {
     }
 }
 
-#[derive(Debug, Default)]
+#[derive(Clone, Debug, Default)]
 pub struct TuiSharedCliOptions(SharedCliOptions);
 
 impl TuiSharedCliOptions {