`xelatex not found` when using `output-ext` different than pdf as Quarto LaTeX engine is not used

Bug description

xelatex is not found when a profile is used.

Steps to reproduce

Use the test.qmd

---
title: "Test"
---

# abc

and _quarto.yml

format:
  latex:
    output-ext: tex
  pdf:
    output-ext: pdf

with the _quarto-test.yml

format:
  latex:
    output-ext: test.tex
  pdf:
    output-ext: test.pdf

and the _metadata.yml

format:
  latex: default # requires such that .tex file is moved to output
  pdf:
    keep-tex: true
    documentclass: scrartcl

then run

quarto render test.qmd

which works fine.

Next run

quarto render test.qmd --profile test

which fails with

xelatex not found. Please select a different --pdf-engine or install xelatex

Expected behavior

Proper rendering when --profile test is used, because obviously xelatex is available (otherwise the default profile would have failed as well)

Actual behavior

xelatex not found when using --profile test on rendering

Your environment

• VSCode 1.93.0
• devcontainer using debian bookworm on MacOS

Quarto check output

Quarto 1.5.56
[✓] 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
[✓] Checking versions of quarto dependencies......OK
[✓] Checking Quarto installation......OK
      Version: 1.5.56
      Path: /opt/quarto/bin

[✓] Checking tools....................OK
      TinyTeX: v2024.09
      Chromium: (not installed)

[✓] Checking LaTeX....................OK
      Using: TinyTex
      Path: /home/user/.TinyTeX/bin/x86_64-linux
      Version: 2024

[✓] Checking basic markdown render....OK

[✓] Checking Python 3 installation....OK
      Version: 3.11.2
      Path: /usr/bin/python3
      Jupyter: (None)

      Jupyter is not available in this Python installation.
      Install with python3 -m pip install jupyter

[✓] Checking R installation...........(None)

      Unable to locate an installed version of R.
      Install R from https://cloud.r-project.org/

Reproduce the issue with test.qmd, _quarto.yml, _quarto-test.yml, and _metadata.yml by running quarto render test.qmd with and without --profile test. Trace how profile format settings select the LaTeX/PDF engine, then verify that the test profile renders successfully without the xelatex error while preserving the requested output extensions.