Rollup merge of rust-lang#82088 - Nicholas-Baron:shorten_html_render, r=GuillaumeGomez

Shorten html::render

The `mod.rs` for librustdoc's `html::render` was over 3,000 lines. This PR reduces it to around 2,300 by
1. Moving `Context` and associated `impl`s to a separate file
2. Moving the `print_item` function and its helpers to a separate file
3. Moving `write_shared` and `write_minify` to their own file

Related to issue rust-lang#60302.
Edit 1: `SharedContext` and related `impl`s is only 72 lines and so will not be moved.

Author: GuillaumeGomez