chore!: update typescript to version `5.6.3`

[david-luna]

Closes: #4870

Checklist:

• [x] Update typescript to 5.6.3
• [x] Document our new minimum typescript version
  • [x] Document a policy for updating typescript in minor versions in the future
• [ ] Add a test project to ensure that minimum typescript version can compile using the updated otel dependencies

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 93.15%. Comparing base (4a394cc) to head (703f0ab). Report is 2 commits behind head on next.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## next #5145 +/- ## ========================================== - Coverage 93.15% 93.15% -0.01% ========================================== Files 315 315 Lines 8113 8111 -2 Branches 1633 1632 -1 ========================================== - Hits 7558 7556 -2 Misses 555 555 ``` | [Files with missing lines](https://app.codecov.io/gh/open-telemetry/opentelemetry-js/pull/5145?dropdown=coverage&src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=open-telemetry) | Coverage Δ | | |---|---|---| | [...es/opentelemetry-instrumentation-grpc/src/utils.ts](https://app.codecov.io/gh/open-telemetry/opentelemetry-js/pull/5145?src=pr&el=tree&filepath=experimental%2Fpackages%2Fopentelemetry-instrumentation-grpc%2Fsrc%2Futils.ts&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=open-telemetry#diff-ZXhwZXJpbWVudGFsL3BhY2thZ2VzL29wZW50ZWxlbWV0cnktaW5zdHJ1bWVudGF0aW9uLWdycGMvc3JjL3V0aWxzLnRz) | `84.61% <ø> (ø)` | | ... and [6 files with indirect coverage changes](https://app.codecov.io/gh/open-telemetry/opentelemetry-js/pull/5145/indirect-changes?src=pr&el=tree-more&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=open-telemetry)

---

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[david-luna]

I starting to think that maybe we need a next branch in the contrib repository so we can sync this type of changes 🤔

[david-luna]

• [ ] Add a test project to ensure that minimum typescript version can compile using the updated otel dependencies

@pichlermarc @dyladan I see a project name esm-http-ts within examples folder. Could that be our testing project? or it's preferable to have something more complex within integration-tests maybe?