feat: render single-dollar and inline double-dollar LaTeX math with KaTeX

[Cl-VII]

Issue for this PR

Related to #40508 (LaTeX rendering in OpenCode). This PR brings ChatGPT-style single-dollar inline math to the web/desktop rendering pipeline, which already renders KaTeX for \(...\) and block ... but not single $...$.

Type of change

• New feature

What does this PR do?

The web/desktop markdown pipeline (packages/ui/src/context/marked-parser.tsx) registers KaTeX extensions for \(...\) (inline) and ... (block, own-paragraph). Model replies commonly use single-dollar inline math ( = \beta_0 + \beta_1 x$) and inline ... — both currently render as raw LaTeX source.

This PR adds two marked inline extensions:

• inlineDollarKatex: renders $...$ via KaTeX
• inlineDoubleDollarKatex: renders inline (non-own-paragraph) ... via KaTeX

Edge cases handled (with tests):

• Currency/placeholder protection: today, .02/GB, $ 5 are left untouched
• Formulas starting with a number still render: (L_{ur}-L_r)\sim\chi^2(Q)$
• Unclosed $ does not swallow the rest of the text (streaming-safe)
• Escaped \$ inside math works
• Formulas do not cross newlines
• The existing block ... (own-paragraph, display mode) and \(...\) behavior is unchanged

How did you verify your code works?

• Added 9 unit tests covering rendering, currency guard, unclosed dollar, escaped dollar, newline boundary, number-leading formulas — all pass (bun test packages/ui: 35/35)
• tsgo --noEmit typecheck passes
• Verified against a full econometrics lecture note (23 formulas: LPM, Probit/Logit, MLE, delta method, LR/Wald tests): all 23 render as KaTeX with zero leftover $ pairs
• Streaming check: partially-streamed $... stays as plain text until closed, then renders — no flicker or swallowed text

Screenshots / recordings

N/A (HTML output verified; KaTeX renders mathml + html dual output for accessibility)

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR

[github-actions]

The following comment was made by an LLM, it may be inaccurate:

Based on the search results, here are the potentially related PRs:

1. PR feat: render LaTeX math as Unicode in TUI #40867 - feat: render LaTeX math as Unicode in TUI

   • Related work on LaTeX rendering, but for TUI instead of web/desktop
   • Addresses the same issue domain (LaTeX math display) but in a different UI layer

2. PR fix(app): render \[...\] LaTeX display math delimiters #35951 - fix(app): render \[...\] LaTeX display math delimiters

   • Earlier fix for LaTeX display math delimiters
   • May be a predecessor to this work

3. PR fix(ui) latex dollar render #38829 - fix(ui) latex dollar render

   • Appears to be a previous attempt at handling dollar-sign LaTeX rendering
   • Could be related or superseded by this PR

The most relevant is PR #40867, which is recent and addresses LaTeX rendering in a complementary way. The other PRs appear to be historical or related attempts at the same problem.

[Cl-VII]

Closing: conflicts with official design decision #34850 (single-dollar math intentionally disabled). Author requested removal.