feat(web/default): Base UI migration and component foundation

Migrate from Radix UI to Base UI, rewrite core UI primitives,
update dependencies (recharts, date-fns, next-themes), add
shadcn agent skill documentation, and refresh AI element components.

This is the foundational work from the v2/localmain lineage that
was not covered by the individual feature commits above.

Author: t0ng7u

.agents/skills/shadcn-ui/SKILL.md

@@ -0,0 +1,105 @@
+---
+name: shadcn-ui
+description: >-
+  Give the assistant project-aware shadcn/ui context: components.json,
+  composition patterns, CLI, registries, theming, and MCP. Use when working on
+  web/default UI, shadcn components, or presets. Overview aligns with
+  https://ui.shadcn.com/docs/skills.md; full upstream skill text is vendored
+  under vendor/shadcn/.
+---
+
+<!-- Canonical overview: https://ui.shadcn.com/docs/skills.md -->
+
+# Skills (shadcn/ui)
+
+Skills give AI assistants project-aware context about shadcn/ui. When used, the assistant knows how to find, install, compose, and customize components using the correct APIs and patterns for your project.
+
+For example, you can ask:
+
+- _"Add a login form with email and password fields."_
+- _"Create a settings page with a form for updating profile information."_
+- _"Build a dashboard with a sidebar, stats cards, and a data table."_
+- _"Switch to --preset [CODE]"_
+- _"Can you add a hero from @tailark?"_
+
+The skill reads your project's `components.json` and provides your framework, aliases, installed components, icon library, and base library so it can generate correct code on the first try.
+
+---
+
+## Install (ecosystem vs this repo)
+
+Official install from [Skills — shadcn/ui](https://ui.shadcn.com/docs/skills.md):
+
+```bash
+npx skills add shadcn/ui
+```
+
+That installs the skill where the `skills` CLI is available. **This repository** keeps the same intent under `.agents/skills/shadcn-ui/` (overview here + **vendored** upstream docs in [`vendor/shadcn/`](./vendor/shadcn/)) and runs the shadcn CLI from the frontend app root:
+
+```bash
+cd web/default && bunx shadcn@latest info --json
+```
+
+Learn more about skills at [skills.sh](https://skills.sh).
+
+---
+
+## What's included (and where)
+
+### Project context
+
+Run **`shadcn info --json`** (here: `cd web/default && bunx shadcn@latest info --json`) for framework, Tailwind version, aliases, base (`radix` | `base`), icon library, installed components, and resolved paths.
+
+### CLI commands
+
+Full command reference (vendored): [`vendor/shadcn/cli.md`](./vendor/shadcn/cli.md).
+
+### Theming and customization
+
+Vendored: [`vendor/shadcn/customization.md`](./vendor/shadcn/customization.md). Live docs: [Theming](https://ui.shadcn.com/docs/theming).
+
+### Registry authoring
+
+Not duplicated as a single file in the vendor tree; see [Registry](https://ui.shadcn.com/docs/registry) and `build` in [`vendor/shadcn/cli.md`](./vendor/shadcn/cli.md).
+
+### MCP server
+
+Vendored: [`vendor/shadcn/mcp.md`](./vendor/shadcn/mcp.md). Live docs: [MCP Server](https://ui.shadcn.com/docs/mcp).
+
+---
+
+## How it works
+
+1. **Project detection** — Applies when `components.json` exists (here: `web/default/components.json`).
+2. **Context injection** — Use `shadcn info --json` as ground truth for imports and APIs.
+3. **Pattern enforcement** — Follow rules in [`vendor/shadcn/SKILL.md`](./vendor/shadcn/SKILL.md) and [`vendor/shadcn/rules/`](./vendor/shadcn/rules/).
+4. **Component discovery** — `shadcn docs`, `shadcn search`, MCP, or registries — see vendored SKILL + MCP doc.
+
+---
+
+## Learn more (web)
+
+- [CLI](https://ui.shadcn.com/docs/cli) — complements [`vendor/shadcn/cli.md`](./vendor/shadcn/cli.md)
+- [Theming](https://ui.shadcn.com/docs/theming)
+- [Registry](https://ui.shadcn.com/docs/registry)
+- [skills.sh](https://skills.sh)
+
+---
+
+## Vendored upstream bundle (deep rules)
+
+Snapshot from [shadcn-ui/ui `skills/shadcn`](https://github.com/shadcn-ui/ui/tree/main/skills/shadcn); revision note in [`vendor/shadcn/UPSTREAM.txt`](./vendor/shadcn/UPSTREAM.txt).
+
+| Doc | Path |
+| --- | --- |
+| Full official skill body | [`vendor/shadcn/SKILL.md`](./vendor/shadcn/SKILL.md) |
+| CLI reference | [`vendor/shadcn/cli.md`](./vendor/shadcn/cli.md) |
+| Theming / customization | [`vendor/shadcn/customization.md`](./vendor/shadcn/customization.md) |
+| MCP | [`vendor/shadcn/mcp.md`](./vendor/shadcn/mcp.md) |
+| Forms | [`vendor/shadcn/rules/forms.md`](./vendor/shadcn/rules/forms.md) |
+| Composition | [`vendor/shadcn/rules/composition.md`](./vendor/shadcn/rules/composition.md) |
+| Icons | [`vendor/shadcn/rules/icons.md`](./vendor/shadcn/rules/icons.md) |
+| Styling | [`vendor/shadcn/rules/styling.md`](./vendor/shadcn/rules/styling.md) |
+| Base vs Radix | [`vendor/shadcn/rules/base-vs-radix.md`](./vendor/shadcn/rules/base-vs-radix.md) |
+
+**Workflow:** Prefer this **root** `SKILL.md` for repo paths (`web/default`, Bun). Read **`vendor/shadcn/SKILL.md`** for the complete upstream workflow, patterns, and CLI quick reference. Use **`vendor/shadcn/rules/*.md`** when validating concrete markup.