📝 Documentation: Consider using tsdocs.dev for deployed site instead of TypeDoc

[JoshuaKGoldberg]

Bug Report Checklist

• I have pulled the latest main branch of the repository.
• I have searched for related issues and found none that matched my issue.

Overview

I learned recently about tsdocs.dev: a really cool initiative to auto-create docs sites for npm packages. It does basically everything the deployed site does or wants to:

• TypeDoc generated docs (what tsdocs.dev is doing on the inside)
  • ...with a nicer looking theme than ours IMO
• Search!
• Version selector

@RebeccaStevens what do you think about pointing users to that site instead of the generated TypeDoc one? That way we can remove all the TypeDoc scaffolding from the build system (🥲).

Additional Info

Issues this would let us close: #144, #150 (maybe), #260

Cold start performance on https://tsdocs.dev/docs/ts-api-utils isn't great. We'll probably want to contribute to the project in some way to help them out. Maybe we should ping the tsdocs.dev url whenever a new package version is released. And/or, I wonder if they're getting overwhelmed with traffic...? 😄

[RebeccaStevens]

From my understanding, tsdocs uses TypeDoc under the hood to generate the page.
So we'll want to keep all the things to do with ensuring we're documenting the code right, but the generation of our docs site can definitely be replaced.