feat(web): add dimmed background scenes behind a tinted-glass interface

[saphid]

Problem

T3 Code's themes set colors, but the workspace is always a flat opaque surface. Bambooed-style
apps show that a calm scene behind a translucent interface makes long sessions feel noticeably
less sterile, and our glass utilities (surface-glass, the glass-opacity setting) already exist
but have nothing scenic behind them to show through.

Change

Every built-in theme ships a matching scenic backdrop (apps/web/public/backgrounds/, one webp
per theme, generated with image generation and compressed to 23-125 KB each). When a scene is
active, a fixed dimmed image paints under every surface, and the main canvas fills re-derive
from the theme's solid colors at partial alpha, so the interface reads as tinted glass over the
scene:

• A themeBackground client setting (auto / none / a built-in theme id) lands in
  packages/contracts. Theme scene follows the active theme, a picked scene sticks across
  theme changes, None turns the backdrop off.
• The scene layer paints on body::before under all content; large surfaces get no
  backdrop-filter (one blurred layer that big repaints on every streaming frame). The scenes
  are generated softly defocused instead.
• Nested bg-background containers stop re-painting while a scene is active, so the glass stays
  a single layer instead of stacking into opacity.
• Terminal fills stay solid; dialogs and popovers keep their existing glass treatment.
• Picker lives in Settings → Appearance → Background scene, searchable as "background scene".
• Dark mode keeps the scene subtle (higher surface opacity + stronger dim) so text contrast on
  the dark palettes is preserved.

Mobile is untouched: it renders its own theme system and palette, and the backdrop piggybacks on
the web theme pipeline. Desktop picks this up automatically since it wraps the web client.

Evidence

Before/after captures of the running client (same workspace, same threads; "before" is the
candidate with the scene set to None, which renders the identical base path):

After (Ocean theme, scene visible through the interface):

After (T3 Chat theme):

Before (scene off):

Settings entry point:

Gap: the screenshot files are captured and ready (/tmp/t3-pr-evidence/) but the file-drop
upload credential was not available in this session, so the images are not yet attached. They
will be uploaded and linked here before the draft leaves draft state.

Verification

• vp test run apps/web/src/themeBackground.test.ts packages/contracts/src/settings.test.ts apps/web/src/components/settings/settingsSearch.test.ts apps/web/src/hooks/useTheme.test.ts — 210 passed.
• pnpm --filter @t3tools/contracts typecheck, pnpm --filter @t3tools/web typecheck — clean.
• vp lint on the touched files — no new warnings (remaining ones pre-date this change).
• Integrated pass in a real client (vp run dev in an isolated worktree, paired browser,
  real workspace data): scene follows theme switches and appearance flips, picker updates live,
  None restores the base rendering, browser chrome theme sync stays correct with the body fill
  cleared.

Model and harness: GLM (enablers/xlarge) via T3 Code / OpenCode, with Codex CLI image generation
for the five scenes and Codex visual QA of the captures.