Investigate Quarto installation needs for `quarto-shiny` app mode

Context

In #64, we added Quarto installation support for quarto-static content (the quarto deploy subcommand requires quarto inspect locally). The quarto-shiny app mode currently maps to the shiny deploy subcommand, so we don't install Quarto for it.

However, it's unclear whether rsconnect-python (via posit connect deploy shiny) needs a local Quarto installation to render/inspect the .qmd before deploying a quarto-shiny app, or whether Connect handles that entirely server-side.

Questions to answer

• Does posit connect deploy shiny for a quarto-shiny app require a local Quarto installation (e.g., for quarto inspect or rendering)?
• If so, should we install Quarto when the app_mode is quarto-shiny in addition to quarto-static?

Current behavior

In src/connect_actions/apptype.py, quarto-shiny maps to deploy type shiny with needs_quarto=False:

APP_MODE_TO_TYPE: dict[str, str] = {
    ...
    "quarto-static": "quarto",
    "quarto-shiny": "shiny",
}

Action items

• Test deploying a quarto-shiny app through the deploy action without Quarto installed locally
• If it fails, update resolve_app_type() to set needs_quarto=True for quarto-shiny
• Add an e2e test for quarto-shiny if support is needed

References

• PR #64 (Install quarto if needed)
• Review discussion

Start in src/connect_actions/apptype.py and review how quarto-shiny currently maps to the shiny deploy type with needs_quarto=False. Test a quarto-shiny deployment through the deploy action without a local Quarto installation; done means either confirming the current behavior or updating resolve_app_type() and adding the requested end-to-end test if Quarto is required.