Upgrade `typescript` to latest v5

[tkajtoch]

Summary

Note: This is a follow-up ticket to #7340, which updates all existing typings to be compatible with the changes introduced in TS v5.

We need to upgrade Typescript to the latest version (5.2.2 or newer).

Acceptance Criteria

• Upgrade the typescript package to the latest v5 version
• Update prop-loader.js to use the updated TypeScript compiler APIs
• Fix any type errors that may come up during the upgrade
• Ensure the application starts (yarn start) and builds (yarn build) without issues

[JasonStoltz]

We may not need to do this, one potential solution is replacing the prop table with storybook. Assigning this as a medium priority.

[auspy]

hi. this is my first time contributing to eui. i am starting with this issue

[github-actions[bot]]

👋 Hi there - this issue hasn't had any activity in 6 months. If the EUI team has not explicitly expressed that this is something on our roadmap, it's unlikely that we'll pick this issue up. We would sincerely appreciate a PR/community contribution if this is something that matters to you! If not, and there is no further activity on this issue for another 6 months (i.e. it's stale for over a year), the issue will be auto-closed.

[JasonStoltz]

Keep it.