Add category filter chips to the tool grid

[varshinivarma16]

Add a row of category filter chips above the tool grid on the homepage. Clicking a chip narrows the grid to that category; All resets it. Each chip shows its count, so the size of each group is visible at a glance.

We now have 43 tools in a single flat grid. Search (Cmd+K) helps when you know the tool's name, but there's no way to browse by type. Categories fix that.

Why

• The grid is getting long — 43 cards with no grouping.
• Search only helps if you already know what you're looking for.
• Counts on each chip make the collection easier to understand.

Proposed categories (covers all 43 tools)

Category	Count	Examples
Format	5	JSON, SQL, XML formatters, Markdown & HTML preview
Convert	10	Base64, URL, YAML↔JSON, curl→fetch, timestamp
CSS	11	Grid, flexbox, gradient, clamp, box shadow, unit converter
Security	6	Hash, bcrypt, JWT, password tools
Generate	5	UUID, QR, cron, gitignore, lorem ipsum
Dev	6	API tester, OpenAPI viewer, regex, diff, HTTP status

Scope

• Add a required category field to every entry in src/constants/tools.ts, plus an exported Category type and CATEGORIES list. Counts are derived from the array, not hardcoded.
• New filter-chip component in src/ui/, built from the existing Button primitive so styling stays consistent.
• Filter state held in src/components/ToolManager.tsx (the homepage island that renders the grid).
• Sync the active category to a query param (/?category=css) so it's linkable and survives a refresh. Uses the browser URL API — no new dependencies.

Not included

No changes to any tool page, no card redesign, no new tools.

[varshinivarma16]

[NRR385]

Hi! I'd like to work on this issue.

I’ll implement the category filter chips, derived category counts, and URL query parameter support as described in the issue.