feat(webui): improve LaTeX rendering with currency detection (#16508)

* webui : Revised LaTeX formula recognition

* webui : Further examples containg amounts

* webui : vitest for maskInlineLaTeX

* webui: Moved preprocessLaTeX to lib/utils

* webui: LaTeX in table-cells

* chore: update webui build output (use theirs)

* webui: backslash in LaTeX-preprocessing

* chore: update webui build output

* webui: look-behind backslash-check

* chore: update webui build output

* Apply suggestions from code review

Code maintenance (variable names, code formatting, string handling)

Co-authored-by: Aleksander Grygier <aleksander.grygier@gmail.com>

* webui: Moved constants to lib/constants.

* webui: package woff2 inside base64 data

* webui: LaTeX-line-break in display formula

* chore: update webui build output

* webui: Bugfix (font embedding)

* webui: Bugfix (font embedding)

* webui: vite embeds assets

* webui: don't suppress 404 (fonts)

* refactor: KaTeX integration with SCSS

Moves KaTeX styling to SCSS for better customization and font embedding.

This change includes:
- Adding `sass` as a dev dependency.
- Introducing a custom SCSS file to override KaTeX variables and disable TTF/WOFF fonts, relying solely on WOFF2 for embedding.
- Adjusting the Vite configuration to resolve `katex-fonts` alias and inject SCSS variables.

* fix: LaTeX processing within blockquotes

* webui: update webui build output

---------

Co-authored-by: Aleksander Grygier <aleksander.grygier@gmail.com>

tools/server/webui/src/stories/fixtures/math-formulas.ts

@@ -1,3 +1,4 @@
+/* eslint-disable no-irregular-whitespace */
 // Math Formulas Content
 export const MATH_FORMULAS_MD = String.raw`
 # Mathematical Formulas and Expressions
@@ -150,6 +151,70 @@ $$\lim_{x \to 0} \frac{\sin x}{x} = 1$$
 
 $$\lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n = e^x$$
 
+## Further Bracket Styles and Amounts
+
+-  \( \mathrm{GL}_2(\mathbb{F}_7) \): Group of invertible matrices with entries in \(\mathbb{F}_7\).
+- Some kernel of \(\mathrm{SL}_2(\mathbb{F}_7)\):
+  \[
+  \left\{ \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix} \right\} = \{\pm I\}
+  \]
+- Algebra:
+\[
+x = \frac{-b \pm \sqrt{\,b^{2}-4ac\,}}{2a}
+\]
+- $100 and $12.99 are amounts, not LaTeX.
+- I have $10, $3.99 and $x + y$ and $100x$. The amount is $2,000.
+- Emma buys 2 cupcakes for $3 each and 1 cookie for $1.50. How much money does she spend in total?
+- Maria has $20. She buys a notebook for $4.75 and a pack of pencils for $3.25. How much change does she receive?
+- 1 kg の質量は
+  \[
+  E = (1\ \text{kg}) \times (3.0 \times 10^8\ \text{m/s})^2 \approx 9.0 \times 10^{16}\ \text{J}
+  \]
+  というエネルギーに相当します。これは約 21 百万トンの TNT が爆発したときのエネルギーに匹敵します。
+- Algebra: \[
+x = \frac{-b \pm \sqrt{\,b^{2}-4ac\,}}{2a}
+\]
+- Algebraic topology, Homotopy Groups of $\mathbb{S}^3$:
+$$\pi_n(\mathbb{S}^3) = \begin{cases}
+\mathbb{Z} & n = 3 \\
+0 & n > 3, n \neq 4 \\
+\mathbb{Z}_2 & n = 4 \\
+\end{cases}$$
+- Spacer preceded by backslash:
+\[
+\boxed{
+\begin{aligned}
+N_{\text{att}}^{\text{(MHA)}} &=
+h \bigl[\, d_{\text{model}}\;d_{k} + d_{\text{model}}\;d_{v}\, \bigr]   && (\text{Q,K,V の重み})\\
+&\quad+ h(d_{k}+d_{k}+d_{v})                                          && (\text{バイアス Q,K,V）}\\[4pt]
+&\quad+ (h d_{v})\, d_{\text{model}}                                 && (\text{出力射影 }W^{O})\\
+&\quad+ d_{\text{model}}                                            && (\text{バイアス }b^{O})
+\end{aligned}}
+\]
+
+## Formulas in a Table
+
+| Area | Expression | Comment |
+|------|------------|---------|
+| **Algebra** | \[
+x = \frac{-b \pm \sqrt{\,b^{2}-4ac\,}}{2a}
+\] | Quadratic formula |
+| | \[
+(a+b)^{n} = \sum_{k=0}^{n}\binom{n}{k}\,a^{\,n-k}\,b^{\,k}
+\] | Binomial theorem |
+| | \(\displaystyle \prod_{k=1}^{n}k = n! \) | Factorial definition |
+| **Geometry** | \( \mathbf{a}\cdot \mathbf{b} = \|\mathbf{a}\|\,\|\mathbf{b}\|\,\cos\theta \) | Dot product & angle |
+
+## No math (but chemical)
+
+Balanced chemical reaction with states:
+
+\[
+\ce{2H2(g) + O2(g) -> 2H2O(l)}
+\]
+
+The standard enthalpy change for the reaction is: $\Delta H^\circ = \pu{-572 kJ mol^{-1}}$.
+
 ---
 
 *This document showcases various mathematical notation and formulas that can be rendered in markdown using LaTeX syntax.*