chore(deps-dev): upgrade to TypeScript 7 (deferred — toolchain not ready)

[Bugs5382]

Summary

Track the TypeScript 6 -> 7 upgrade. It was attempted in isolation and
deferred: the current toolchain is not yet compatible with the TypeScript 7
native compiler.

Blockers found (TypeScript 7.0.2)

1. typedoc crashes. npm run typedoc fails with
   TypeError: Cannot read properties of undefined (reading 'PropertyDeclaration').
   typedoc 0.28 (with @shipgirl/typedoc-plugin-versions) reads TypeScript
   compiler-API internals that the TS 7 native rewrite restructured. This is
   upstream and blocks the docs build.
2. Build emits TS6059 rootDir errors (x48). TS 7 is stricter about
   rootDir: each package tsconfig.json includes ../../__tests__/<pkg>,
   which sits outside the package rootDir. tsdown still emits, but the errors
   are noisy and would fail a stricter gate.

Acceptance criteria

• Re-attempt once typedoc (and @shipgirl/typedoc-plugin-versions) support
  TypeScript 7.
• Resolve the TS6059 rootDir/include mismatch in the package tsconfigs.
• npm run build, npm test, and npm run typedoc all pass on TypeScript 7.

Notes

Independent of TS 7, npm run typedoc currently also fails on TypeScript 6 due
to a pre-existing type error in __tests__/client/hl7.client.test.ts (a client
call missing the required version). Worth fixing alongside, and wiring a docs
step into CI so it cannot regress unnoticed.