chore: update vue-tsc 2.0

[VividLemon]

Clear and concise description of the problem

vue-tsc needs to be updated. The following needs to occur:

1. "type-check": "vue-tsc --build --force", replace the script in bvn to this
2. Tsconfigs need to be updated:

Merge ours with the following:

{
  "extends": "@vue/tsconfig/tsconfig.dom.json",
  "include": ["env.d.ts", "src/**/*", "src/**/*.vue"],
  "compilerOptions": {
    "composite": true,
    "tsBuildInfoFile": "./node_modules/.tmp/tsconfig.app.tsbuildinfo",

    "baseUrl": ".",
  }
}

{
  "extends": "@tsconfig/node20/tsconfig.json",
  "include": [
    "vite.config.*",
    "vitest.config.*",
    "cypress.config.*",
    "nightwatch.conf.*",
    "playwright.config.*"
  ],
  "compilerOptions": {
    "composite": true,
    "noEmit": true,
    "tsBuildInfoFile": "./node_modules/.tmp/tsconfig.node.tsbuildinfo",

    "module": "ESNext",
    "moduleResolution": "Bundler",
    "types": ["node"]
  }
}

{
  "extends": "./tsconfig.app.json",
  "exclude": [],
  "compilerOptions": {
    "composite": true,
    "tsBuildInfoFile": "./node_modules/.tmp/tsconfig.vitest.tsbuildinfo",

    "lib": [],
    "types": ["node", "jsdom"]
  }
}

Some things are not to be merged. For example, we don't use jsdom.

Once that is done, the build errors need to be fixed.

Suggested solution

n

Alternative

No response

Additional context

pnpm create vue@3 to create a blank template, then merge in some of the structural changes.

Other packages need to be updated as well if they haven't already (playground, etc)

Validations

• Follow our Code of Conduct
• Read the Contributing Guide.
• Check that there isn't already an issue that request the same feature to avoid creating a duplicate.

[VividLemon]

If #1810 hasn't been merged yet by the time this is finished, rebase and request to push into that branch. Either #1810 goes out standalone, or this goes with #1810

[sceee]

Just wanted to note here that I experienced errors when updating to vue-tsc v2 in a project using bootstrap-vue-next and created this issue for it in vuejs/language-tools which is not yet resolved as of today:
vuejs/language-tools#4026

[VividLemon]

I'm aware, although, I don't believe that is their issue. I believe it's more of a setup issue. But I may be wrong. V2 has been a bit messy. I expected it to be somewhat simple based on the changelog, but has issues like described which has been unpleasant.