Add ESLint flat config to backend.ai-client package

[yomybaby]

Context

packages/backend.ai-client/package.json declares:

"lint": "eslint ./src --max-warnings=0",
"prepublishOnly": "pnpm lint && pnpm test && pnpm build"

There is no eslint.config.js (or any .eslintrc*) inside the package. Depending on how ESLint resolves config, the lint script either no-ops or picks up the repo root config and applies React/JSX rules that do not match a TypeScript-only library. Either way, prepublishOnly is currently giving a misleading green light.

Scope

• Add packages/backend.ai-client/eslint.config.js (flat config, ESM)
• Use the shared packages/eslint-config-bai if it has a non-React preset, otherwise extend @eslint/js + typescript-eslint directly
• Recommended initial rule set:
  • @typescript-eslint/recommended
  • @typescript-eslint/consistent-type-imports: error
  • no-floating-promises (or @typescript-eslint/no-floating-promises): error
  • @typescript-eslint/no-explicit-any: warn (kept as warn for now — strict typing pass is a separate ticket)
• Ignore dist/, *.test.ts for the strict subset if needed
• Confirm pnpm --filter backend.ai-client lint runs and reports honestly (warnings allowed but no errors)

Verification

• pnpm --filter backend.ai-client lint exits 0 with the new config (after fixing only quick wins; any warnings expected)
• bash scripts/verify.sh passes
• New errors introduced afterwards would actually fail prepublishOnly

Out of scope

• Removing all any (separate issue, large scope)
• Tightening tsconfig.strict (separate issue)

JIRA Issue: FR-2790