[Maintenance] Replace or support vue-tsc with typed checks of @vue/eslint-config-typescript

[devtobi]

Relevant template

refarch-frontend, refarch-webcomponent

Problem description (optional)

We currently use vue-tsc to type check the source code when running the lint job
Additionally we use vue-tsc in the build job to support features like incremental builds

With the recently newly upgraded @vue/eslint-config-typescript we might be able to replace vue-tsc and even improve linting capability in TypeScript code as it looks like that @vue/eslint-config-typescript includes more rules.

Desired solution

We need to investigate if the new type check solution of @vue/eslint-config-typescript could replace the use of vue-tsc.
If so vue-tsc should be removed as a dependency and from direct calls inside the build script.

Considered alternatives (optional)

Run both tools in parallel, if we would loose features like incremental builds when removing vue-tsc

Additional context (optional)

See https://github.com/vuejs/eslint-config-typescript?tab=readme-ov-file#linting-with-type-information for more information about typed checks in @vue/eslint-config-typescript

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