feat(mobile-web): render math formulas with katex in chat markdown

[BingCHuanJ]

Summary

Adds KaTeX math rendering support (remark-math and rehype-katex) to chat markdown messages in mobile-web. It supports inline ($...$, \(...\)) and block ($$...$$, \[...\]) LaTeX formulas with mobile-responsive horizontal scrolling.

Type and Areas

Type: Feature

Areas: mobile web

Motivation / Impact

Currently, LaTeX math formulas sent in remote control chats are displayed as raw text (e.g., $\alpha$ or $$\sum_{i=1}^n x_i$$), making technical discussions and math responses hard to read on mobile devices.

This PR adds:

• TeX formula rendering using katex, remark-math, and rehype-katex.
• Delimiter normalization (\(...\) -> inline math, \[...\] -> display math) with code-fence and inline-code protection.
• Responsive styling for .katex-display with horizontal scrolling and max-width bounds to prevent layout overflow on narrow mobile screens.

Review updates

• KaTeX stays off the chat chunk. The math plugins and styles live in MarkdownMathContent.tsx, which ChatMarkdown imports on demand. The chat chunk stays near its pre-PR size; the ~280 kB KaTeX chunk is only fetched for messages that may contain math.
• Currency and shell text stay literal. remark-math runs with singleDollarTextMath: false, and only recognized formulas are widened to the $$...$$ form it still parses. This keeps $5 and $10, $HOME, ${VAR}, and Windows paths as text even when the same message also contains formulas, and it prevents a \(...\) conversion from pairing with an earlier currency dollar.
• Display math respects its container. $$...$$/\[...\] become a block only when they own a top-level line; inside lists, tables, and blockquotes they stay inline so the surrounding container is not torn apart.
• Delimiter logic is testable. Activation and normalization moved to the pure chatMarkdownMath.ts, with coverage for escaped delimiters, blockquoted/indented code fences, multi-backtick code, code-fence $$/$& payloads, currency, shell variables, and Windows paths.
• Dependency cleanup. Removed the redundant @types/katex devDependency; katex ships its own type definitions.

Verification

• pnpm --dir src/mobile-web run type-check: passed with zero type errors.
• pnpm --dir src/mobile-web run test:ui-components: passed (18/18, including lazy-load contracts, currency/shell gating, container-aware display math, and code isolation).
• pnpm --dir src/mobile-web run test:host-queue: passed (17/17, including real-browser KaTeX DOM, mixed currency/formula text, and code-fence preservation).
• pnpm --dir src/mobile-web run test:session-stream-browser: passed.
• pnpm --dir src/mobile-web run build: emits a separate MarkdownMathContent JS/CSS chunk.
• pnpm run check:repo-hygiene: passed.

Reviewer Notes

• Uses katex/dist/katex.min.css bundled with font handling compatible with mobile assets; the CSS is emitted with the lazy math chunk.
• Formula display blocks (.katex-display) are constrained to viewport bounds with -webkit-overflow-scrolling: touch for smooth touch scrolling.
• A bare single-dollar identifier longer than two characters ($abc$) is treated as text, not math, to avoid swallowing shell variables. Formulas should use TeX markers ($x^2$, $\alpha$) or two-character identifiers ($x$, $n$).
• $$content with content on the opening line and the closing fence on a later line is left untouched; standard $$ fences and single-line $$...$$ are supported.

Checklist

• This PR is focused and does not include secrets, temporary prompts, generated scratch files, or unrelated artifacts.
• Relevant verification is recorded above, or skipped checks are explained.
• User-facing strings, docs, and locales are updated where applicable.