Add `vite-ts-lib-starter` to starter templates

Please make sure all the requirements are satisfied, otherwise the PR could be closed without further notice.

Checklist

[x] Title as described.
[x] Make sure you put things in the right category.
[x] The description of your item should be a sentence with less than 24 words.
[x] Avoid using links and parentheses in description.
[x] Omit unnecessary words already provided in the context (e.g. for Vite, a Vite plugin).
[x] Use proper case for terms (e.g. GitHub, TypeScript, ESLint, etc.)
[x] When mentioning tools, omit versions whenever possible (e.g. use TypeScript instead of TypeScript 4.x, but keep Vue 2 and Vue 3 as they're incompatible).
[x] When mentioning package names, use quotes whenever possible.
[x] Always add your items to the end of a list.

[ ] The plugin/tool is working with Vite 2.x and onward.
[ ] The project is Open Source.
[ ] The project follows the Vite Plugins Conventions.
[ ] The plugin uses Vite-specific hooks and can't be implemented as a Compatible Rollup Plugin.
[ ] The repo should be at least 30 days old.
[ ] The documentation is in English.
[ ] The project is active and maintained (inactive projects for longer 6 months will be removed without further notice).
[ ] The project accepts contributions.
[ ] Not a commercial product.

[x] The starter template is working with Vite 2.x and onward.
[x] The documentation is in English.
[x] The starter template must provide enough instructions / documentation about how to start up and what's included.
[x] A screenshot or a live demo should be included.
[ ] The repo should be at least 30 days old.
[x] Should be differentiable from the existing starter templates.

[ ] The website is available without errors and load in a reasonable amount of time.
[ ] The website must be Open Source and showing it's using Vite intensively.
[ ] The website is original and not too simple. For that reason, blogs and simple landing pages are rejected.