Migrate typecheck to TypeScript 7 RC

[Kashkovsky]

Summary

• Add an exact typescript-7 alias for typescript@7.0.1-rc.
• Keep typescript@^6.0.3 for typescript-eslint's current JS API and peer range.
• Run npm run typecheck through node ./node_modules/typescript-7/bin/tsc so project typechecking uses the TS 7 RC compiler.

Detail
typescript-eslint@8.62.x still peers on typescript >=4.8.4 <6.1.0 and imports the stable typescript JS API. Installing typescript@7.0.1-rc as the primary typescript package breaks lint because the TS 7 RC package exposes tsc but does not expose that stable CommonJS API.

This uses the side-by-side layout instead: TS 6 remains the package consumed by lint tooling, while the project typecheck script invokes the TS 7 compiler alias directly.

Test plan

node ./node_modules/typescript-7/bin/tsc --version
npm run typecheck --silent
npm run lint --silent
npm run test --silent
npm run build --silent
npm run prettier:check --silent

Precommit also ran npm run lint, npm run prettier:write, and npm run test.