Better loading page while a package is first building?

[JoshuaKGoldberg]

Upon publishing a new version of an npm package, it seems like initial versions of the package take a while to build before they're cached. For example, when https://tsdocs.dev/docs/ts-api-utils/1.2.0 was released just now, on visiting https://tsdocs.dev/docs/ts-api-utils for the first minute or it would stall and maybe eventually give a Cloudflare 524 timeout. Now both pages are working fine.

Separate from speeding up the package builds (#44): could the site immediately give a 'loading' page while the package version is building?