VSCode Extension : Preview not working as expected for websites

Bug description

quarto preview redirects browsers to the actively edited ('saved') document: for any page saved across website projects.
VSCode extension has a Preview button + a "Render on Save" option, but since the button initiates a quarto preview path/to/file.qmd in all cases, then it only ever reacts to saves to a single page (from which the button was clicked), as opposed to across pages - as quarto preview does

The extension Preview button doesn't correspond to what I expect from quarto preview (since it does quarto preview path/to/file.qmd)

I don't use the extension because quarto preview behavior is a better workflow for me when working with websites.

Perhaps Preview is an ambiguous UI and either behavior is arguably correct. But I am stating specifically what I expected, plus behavior from vanilla quarto preview. (and this despite the title - so feel free to close if you disagree)

I don't use the extension because I cannot reproduce the experience of quarto preview inside it when working with websites, which is my preferred workflow.

ref #6440

Steps to reproduce

First turn on Render on Save in extension

then

quarto create
# then select project, website, name: the-website
cd the-website
code .
# press Preview button on index.qmd
# edit abount.qmd

Expected behavior

Preview pane redirects to re-rendered about.qmd

Actual behavior

nothing: no render or redirect

Your environment

vscode 1.90.2

on ubuntu 22.04

Quarto check output

Quarto 1.5.47
[✓] Checking versions of quarto binary dependencies...
      Pandoc version 3.2.0: OK
      Dart Sass version 1.70.0: OK
      Deno version 1.41.0: OK
      Typst version 0.11.0: OK

extension v1.113.0

quarto-dev / quarto