Refactor methods implemented using Site.prototype

[jovyntls]

Please confirm that you have searched existing issues in the repo

Yes, I have searched the existing issues

Is your feature request related to a problem? Please describe.

Currently, we implement a few methods using Site.prototype (here) due to incompatibility with ES6 class syntax.
This is slightly confusing, especially since we need to stub out the method signatures to maintain TS compatibility.

Describe the solution you'd like

If it is possible, let's implement these as class methods for consistency and readability.

Additional context

• See Adopt ES6 class syntax #979 for the reasoning behind using Site.prototype.xxx
• Relevant context on the reasoning for stubbing out the method signatures