Add lint checks in CI and update ESLint to next major version

[raducristianpopa]

We currently do not have lint checks in CI and this is breaking the current ESLint scripts.

Originally posted by @raducristianpopa in #297 (comment)

• chore(ci/pr-checks): add lint checks #306
• Update eslint

[sidvishnoi]

Ok the eslint ecosystem isn't ready yet for upgrade. We can write more code to make it work, but not worth it. I tried, and failed.
We'll get enough unmet peer dependencies warnings, and the legacy/compat packages don't work too well together - missing warnings, false positives.
For migration, I used https://eslint.org/blog/2024/05/eslint-configuration-migrator/, it was helpful, but still missing warnings.

So, let's keep it in backlog.

[sidvishnoi]

Update: All plugins except following now support eslint v9:

typescript-eslint v8 (presently in beta) supports v9.

├─┬ eslint-plugin-jest 28.6.0
│ ├── ✕ unmet peer @typescript-eslint/eslint-plugin@"^6.0.0 || ^7.0.0": found 8.0.0-alpha.30
│ └─┬ @typescript-eslint/utils 7.13.0
│   └── ✕ unmet peer eslint@^8.56.0: found 9.5.0
├─┬ eslint-plugin-jsx-a11y 6.9.0
│ └── ✕ unmet peer eslint@"^3 || ^4 || ^5 || ^6 || ^7 || ^8": found 9.5.0
├─┬ eslint-plugin-react 7.34.3
│ └── ✕ unmet peer eslint@"^3 || ^4 || ^5 || ^6 || ^7 || ^8": found 9.5.0
├─┬ eslint-plugin-react-hooks 4.6.2
│ └── ✕ unmet peer eslint@"^3.0.0 || ^4.0.0 || ^5.0.0 || ^6.0.0 || ^7.0.0 || ^8.0.0-0": found 9.5.0