0.1.83: request 1-hour prompt cache (token fix), context chip above prompt box

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Token cost: request the 1-hour prompt cache

The app set no cache TTL, so on API-key auth Claude defaults to the 5-minute cache. In a long conversation with minutes between turns, the cache dies between turns and every turn re-bills the entire history at full input price instead of the 0.1× cache read.

Set ENABLE_PROMPT_CACHING_1H=1 on Claude runs. The CLI exposes no per-request TTL flag — this env var is the only lever (same mechanism the abstraction uses for MAX_THINKING_TOKENS). Cache reads refresh the window for free, so an active session rarely pays the higher 1h write more than once. No-op on subscription auth (the CLI already requests 1h there).

Stacks on #98 (static system prompt → cacheable). Together: the history is written to cache once and read at 0.1× for up to an hour, instead of re-billed in full every turn.

UI: context chip above the prompt box

Moved from an in-box top-right corner chip (which overlapped text while typing a long line) to its own right-aligned row above the prompt box.

Verify

• cargo test -p az-gui — 130 pass, fmt/clippy clean
• bun run typecheck + biome check clean, bun run test:run — 318 pass
• After merge, confirm on a continuing conversation: cache-read tokens should stay high across replies minutes apart (the 5m cache would have gone cold); the "cache miss?" chip should stop appearing.