Hi, I try to install this extension under ubuntu22.04.

The JdbcOOo step is ok; I have also desinstalled the two libraries you suggested (libhsqldb1.8.0-java and the other)
update of python modules ok: setuptools (73.0.1), six(1.16.0), packaging(24.1)

Meanwhile there is a first strange thing: in LO Outils > Options > … > Info système:
setuptools is marked obsolete while it's newer than required:
7348 2024-08-23 10:00:14.717728362 LogManager::logInfos(): AVERTISSEMENT: Le paquet Python version 73.0.1 semble être obsolète, la version minimale est 72.1.0. L'emplacement de l'installation est: /home/boris/.local/lib/python3.10/site-packages/_distutils_hack/init.py
(Even with the specific 72.1.0 version, the following part happens)

After that, an installation attempt for HyperSQLOOo.oxt fails with the following:

ERROR: Exception occurred: <class 'ImportError'>: cannot import name 'g_path' from 'hypersql.configuration' (/var/spool/libreoffice/uno_packages/cache/uno_packages/lu127544ykr4.tmp_/HyperSQLOOo.oxt/service/pythonpath/hypersql/configuration.py) (or 'documenthandler.DocumentHandler' is unknown), traceback follows
  File "/usr/lib/libreoffice/program/pythonloader.py", line 146, in writeRegistryInfo
    mod = self.getModuleFromUrl( locationUrl )
  File "/usr/lib/libreoffice/program/pythonloader.py", line 101, in getModuleFromUrl
    exec(codeobject, mod.__dict__)
  File "/var/spool/libreoffice/uno_packages/cache/uno_packages/lu127544ykr4.tmp_/HyperSQLOOo.oxt/service/OptionsHandler.py", line 37, in <module>
    from hypersql import OptionsManager
  File "/usr/lib/python3/dist-packages/uno.py", line 349, in _uno_import
    return _builtin_import(name, *optargs, **kwargs)
  File "/var/spool/libreoffice/uno_packages/cache/uno_packages/lu127544ykr4.tmp_/HyperSQLOOo.oxt/service/pythonpath/hypersql/__init__.py", line 30, in <module>
    from . import sdbc
  File "/usr/lib/python3/dist-packages/uno.py", line 349, in _uno_import
    return _builtin_import(name, *optargs, **kwargs)
  File "/var/spool/libreoffice/uno_packages/cache/uno_packages/lu127544ykr4.tmp_/HyperSQLOOo.oxt/service/pythonpath/hypersql/sdbc/__init__.py", line 30, in <module>
    from .driver import Driver
  File "/usr/lib/python3/dist-packages/uno.py", line 349, in _uno_import
    return _builtin_import(name, *optargs, **kwargs)
  File "/var/spool/libreoffice/uno_packages/cache/uno_packages/lu127544ykr4.tmp_/HyperSQLOOo.oxt/service/pythonpath/hypersql/sdbc/driver.py", line 33, in <module>
    from ..driver import Driver as DriverBase
  File "/usr/lib/python3/dist-packages/uno.py", line 349, in _uno_import
    return _builtin_import(name, *optargs, **kwargs)
  File "/var/spool/libreoffice/uno_packages/cache/uno_packages/lu127544ykr4.tmp_/HyperSQLOOo.oxt/service/pythonpath/hypersql/driver.py", line 41, in <module>
    from .documenthandler import DocumentHandler
  File "/usr/lib/python3/dist-packages/uno.py", line 426, in _uno_import
    raise uno_import_exc
  File "/usr/lib/python3/dist-packages/uno.py", line 349, in _uno_import
    return _builtin_import(name, *optargs, **kwargs)
  File "/var/spool/libreoffice/uno_packages/cache/uno_packages/lu127544ykr4.tmp_/HyperSQLOOo.oxt/service/pythonpath/hypersql/documenthandler.py", line 57, in <module>
    from .configuration import g_path

… and indeed, in the documenthandler.py (HyperSQLOOo/uno/lib/uno/embedded/documenthandler.py), there is a line to try loading this variable, but it doesn't exist in configuration.py.