DoxySphinx ignores HTML_OUTPUT and always expects Doxygen output in html

[selineleupi]

In doxysphinx/doxygen.py the output directory is currently resolved as:

out = Path(doxygen_cwd) / str(config["OUTPUT_DIRECTORY"]) / "html" # config["HTML_OUTPUT"]
This appears to ignore the Doxygen HTML_OUTPUT configuration value and instead always assumes that the generated HTML output directory is named html. As a result, Doxyfile configurations such as:

OUTPUT_DIRECTORY = output
HTML_OUTPUT = myProjectOutput

are resolved by doxysphinx as output/html instead of output/myProjectOutput.

Why is this problematic?
A common use case is generating documentation for multiple projects or languages, for example:

    output
         ├── cpp_html/
         └── java_html/

with separate Doxyfiles and configurations.
This allows documentation to remain separated and avoids overwriting generated content.
Because DoxySphinx currently appears to require html, it becomes difficult or impossible to use multiple Doxygen output directories within the same Sphinx documentation tree.

Suggested fix:
Respect the configured HTML_OUTPUT value:

out = (
    Path(doxygen_cwd)
    / str(config["OUTPUT_DIRECTORY"])
    / str(config["HTML_OUTPUT"])
)

and fall back to "html" only when HTML_OUTPUT is not explicitly configured, matching Doxygen's default behavior.

[selineleupi]

Further investigation suggests that the issue affects both discovery of the Doxygen HTML output and resource copying. While pages are generated into the expected Sphinx output location, Doxygen assets (SVG, CSS, JS) continue to be copied to a hardcoded html directory. This causes pages generated for custom HTML_OUTPUT directories to lose styling, diagrams, inheritance graphs and other Doxygen functionality because the referenced assets are no longer colocated with the generated HTML pages.