Update Typescript

[dyladan]

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Selected option 2

• [ ] Update typescript to 5.x
• [ ] Document our new minimum typescript version
  • [ ] 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

Option 1 - Update and downlevel types

• [ ] Update typescript to latest 4.x version
• [ ] Use downlevel-dts to downlevel types to 4.4 (previously supported version)
• [ ] Use typesVersions so that old Typescript versions use 4.4 types
• [ ] Add a test project to ensure that typescript 4.4 can compile using the updated otel dependencies
• [x] Close #2329 if not already closed

Option 2 - Update and raise our minimum typescript version

• [ ] Update typescript to some later version that allows us to update our dependencies (see https://github.com/open-telemetry/opentelemetry-js/pull/4834)
• [ ] Document our new minimum typescript version
• [ ] Possibly log warnings before we actually make this change in order to give users who will be broken a warning