feat(mcp): add Codex session support - #949

Verify each finding against the current code and only fix it if needed.

Inline comments:
In `@apps/mcp/README.md`:
- Line 66: Update the README sentence that references CODEX_HOME to explicitly
state that session files live in the sessions/ subdirectory and show the
resolved default; replace the current line with wording like: "Codex session
usage must be read from ${CODEX_HOME:-~/.codex}/sessions/, with CODEX_HOME
resolved and defaulting to ~/.codex" so it mentions the sessions/ directory and
the resolved default for CODEX_HOME.

In `@apps/mcp/src/cli-utils.ts`:
- Around line 20-40: resolveBunExecutable currently only checks for "bun" and
probes node_modules/.bin/bun, which misses Windows variants; update
resolveBunExecutable to consider platform-specific executable names (e.g., on
Windows check "bun.exe" and "bun.cmd" in addition to "bun"), expand the probe
loop that builds candidate paths (the variable candidate) to test each name
variant using pathExists, and when inspecting process.execPath (used in the
currentExecutable check) compare its basename against the same set of variants
so installed shims are detected; ensure the function still returns the first
existing candidate or falls back to 'bun' if none are found.

In `@apps/mcp/src/command.ts`:
- Around line 103-110: The header suppression currently only triggers for
explicit '--type' / '-t' with the next token 'stdio'; change the logic so
renderHeader is also suppressed when stdio is provided as a single-token flag
(e.g. '--type=stdio' or '-t=stdio') and when no type flag is provided (default
stdio). Update the computation around stdioIndex/args used before calling cli
(the variables stdioIndex, args, and the renderHeader option passed to
cli/mcpCommand) to treat any of these cases as stdio: (1) existing '--type' or
'-t' followed by 'stdio', (2) '--type=stdio' or '-t=stdio' tokens, or (3)
absence of any '--type'/'-t' flag (no type specified) — then set suppressHeader
true so renderHeader becomes null.

In `@apps/mcp/src/mcp-utils.ts`:
- Around line 5-9: Replace the try/catch in defaultOptions with the
`@praha/byethrow` Result pattern: call Result.try({ try: () => getClaudePaths(),
catch: (err) => err })(), then use Result.isFailure(result) to detect errors and
return { claudePath: '' } as const satisfies LoadOptions on failure; otherwise
use result.value[0] ?? '' to build and return the LoadOptions object; reference
getClaudePaths(), defaultOptions(), Result.try and Result.isFailure when
applying the change.

---

Nitpick comments:
In `@apps/mcp/src/cli-utils.test.ts`:
- Around line 1-4: Move the external test file into an in-source Vitest block
inside apps/mcp/src/cli-utils.ts by copying the tests from
apps/mcp/src/cli-utils.test.ts into a new if (import.meta.vitest != null) { ...
} section in cli-utils.ts; update references to createFixture and any imports so
they are scoped inside that block, remove the standalone .test.ts file, and
ensure the tests import CLI functions directly from the same module (e.g.,
functions exported by cli-utils.ts) so the in-source tests run under
import.meta.vitest.

In `@apps/mcp/src/cli-utils.ts`:
- Around line 16-18: The function pathExists is exported but only used
internally by resolveBunExecutable, so remove the export to make it file-private
(rename/export removal for pathExists) and update any internal references to the
now-internal function; also remove the redundant test spy that was targeting
pathExists since the Bun-runtime branch returns before filesystem lookup and the
spy is unnecessary. Ensure resolveBunExecutable still calls the (now
non-exported) pathExists and adjust imports/usages elsewhere if any were relying
on the export.

In `@apps/mcp/src/codex.ts`:
- Around line 141-144: The three functions getCodexDaily, getCodexMonthly, and
getCodexSession call runCodexCliJson(...) and then use raw JSON.parse(...)
directly; change these to use Result.try() around the parse+schema.parse step to
capture parse errors (e.g. Result.try(() => schema.parse(JSON.parse(raw)))) and
return/propagate the Result. To avoid duplication, add a small helper like
parseCodexResponse(raw, schema) that performs Result.try(() =>
schema.parse(JSON.parse(raw))) and use it from getCodexDaily
(codexDailyResponseSchema), getCodexMonthly (codexMonthlyResponseSchema) and
getCodexSession (codexSessionResponseSchema), keeping runCodexCliJson usage
unchanged.

In `@apps/mcp/src/mcp.ts`:
- Around line 253-256: The test for createMcpServer with claudePath:'' only
checks construction; extend it to exercise the MCP tools end-to-end by invoking
one or both tools (e.g., the 'daily' and/or 'session' tool handlers exposed by
the created server) and asserting their responses when no data exists; locate
the test that calls createMcpServer, retrieve the server.tools (or the exported
tool call functions) and perform a tool invocation (e.g., call daily/session
with an appropriate empty or minimal request) and assert the expected fallback
behavior (error/empty result/default message) to verify empty claudePath
handling.

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Inline comments:
In `@apps/mcp/README.md`:
- Line 88: The img tag for the sponsors badge lacks an alt attribute; update the
<img> element (the sponsors SVG included in README.md) to include a concise,
descriptive alt text (e.g., "Project sponsors" or "Sponsors logos") so screen
readers can convey the image purpose and improve accessibility.