feat(@browser-ai/core): rename input usage

[mikechao]

This PR addresses #150

Because @types/dom-chromium-ai has not yet shipped the new names, yet, dom-chromium-ai-augmentation.d.ts was created to fill this gap.

src/dom-chromium-ai-augmentation.d.ts (new)
Merges the four new members into the existing global LanguageModel interface via TypeScript declaration merging. No types are duplicated or overridden — the new names simply sit alongside the old ones that @types/dom-chromium-ai already provides. Once the upstream package ships the new names, this file can be deleted with no other changes required.

Runtime changes

• Session event registration now detects support at runtime: registers contextoverflow when "oncontextoverflow" in session, falls back to quotaoverflow for older Chrome builds.
• getContextUsage() and getContextWindow() read contextUsage/contextWindow with ?? inputUsage/?? inputQuota as a fallback, so both old and new Chrome builds work correctly.
• onContextOverflow is the new option name; onQuotaOverflow is retained as a @deprecated alias that resolves through the same code path.

Public API changes (@browser-ai/core)

• getContextUsage() / getContextWindow() — new methods (replace getInputUsage() / getInputQuota())
• onContextOverflow — new setting (replaces onQuotaOverflow)
• Old names kept as @deprecated aliases for backward compatibility

Other files updated

• examples/next-hybrid — updated to use new method and option names
• docs/content/docs/ai-sdk-v6/core/api-reference.mdx — updated API reference
• test/session-manager.test.ts — 33 tests, all passing (3 new tests cover fallback paths and deprecated alias behaviour)

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[jakobhoeg]

Thank you @mikechao! Mind resolving the merge conficts? I just pushed a small refactor

[mikechao]

Hi @jakobhoeg

I updated the main branch and rebased these changes on top it.

[jakobhoeg]

LGTM. Thank you!