Refactor prompt buffer handling

[aadcg]

Description

Fixes #3489.

Checklist:

• Git branch state is mergable.
• Changelog is up to date (via a separate commit).
• New dependencies are accounted for.
• Documentation is up to date.
• Compilation and tests ((asdf:test-system :nyxt/<renderer>))
  • No new compilation warnings.
  • Tests are sufficient.

[aadcg]

I'm not happy with this iteration, since it adds even more lag to each prompt buffer invocation. Thinking.

[aadcg]

Due to #3523, it is not possible to pursue this strategy that proposed creating a webview on each prompt buffer invocation.

Superseded by bac6949.