Use TypeScript 6

[jsteinich]

Description

TypeScript 6 has recently been released, but the project doesn't currently use or fully support it.
Some aspects to fix / look into:

• Support in init template
  • This was recently disabled due to an upstream dependency conflict.
• Use in the library itself
  • Need to solve the same problems as the init template due to the same dependency being used.
• May need changes in JSII for support
• Handle breaking changes

References

No response

Help Wanted

• I'm interested in contributing a fix myself

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