Render math in chat messages with KaTeX

Add a marked extension that tokenizes math delimiters and renders them
with KaTeX: `$$ ... $$` / `\[ ... \]` as block, `$ ... $` / `\( ... \)`
and mid-paragraph `$$ ... $$` as inline.

Inline `$ ... $` requires a non-space after the opening `$`, no newline
inside, and a non-digit after the closing `$`, so prose like "$100 から
$200" is left alone; `\$` still escapes a literal dollar sign. Parse
errors fall back to KaTeX's red inline message instead of throwing, and
math whose closing delimiter has not streamed in yet stays plain text.

DOMPurify strips `semantics` and `annotation` by default, which would
leak the raw TeX out of KaTeX's MathML output, so both are allowed
explicitly.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

frontend/package-lock.json

@@ -9,6 +9,7 @@
       "version": "0.1.0",
       "dependencies": {
         "dompurify": "^3.1.0",
+        "katex": "^0.16.47",
         "marked": "^12.0.0",
         "pinia": "^2.1.7",
         "vue": "^3.4.0",
@@ -1117,6 +1118,15 @@
         "balanced-match": "^1.0.0"
       }
     },
+    "node_modules/commander": {
+      "version": "8.3.0",
+      "resolved": "https://registry.npmjs.org/commander/-/commander-8.3.0.tgz",
+      "integrity": "sha512-OkTL9umf+He2DZkUq8f8J9of7yL6RJKI24dVITBmNfZBmri9zYZQrKkuXiKhyfPSu8tUhnVBB1iKXevvnlR4Ww==",
+      "license": "MIT",
+      "engines": {
+        "node": ">= 12"
+      }
+    },
     "node_modules/csstype": {
       "version": "3.2.3",
       "resolved": "https://registry.npmjs.org/csstype/-/csstype-3.2.3.tgz",
@@ -1242,6 +1252,22 @@
         "he": "bin/he"
       }
     },
+    "node_modules/katex": {
+      "version": "0.16.47",
+      "resolved": "https://registry.npmjs.org/katex/-/katex-0.16.47.tgz",
+      "integrity": "sha512-Eeo8Ys1doU1z+x8AZsPpQu+p/QcZBI5PeOo7QGQdy2x2m0MU/hYagBbGOmXwr5KVbEfVuWv9LpnQWeehogurjg==",
+      "funding": [
+        "https://opencollective.com/katex",
+        "https://github.com/sponsors/katex"
+      ],
+      "license": "MIT",
+      "dependencies": {
+        "commander": "^8.3.0"
+      },
+      "bin": {
+        "katex": "cli.js"
+      }
+    },
     "node_modules/magic-string": {
       "version": "0.30.21",
       "resolved": "https://registry.npmjs.org/magic-string/-/magic-string-0.30.21.tgz",