hatch build (but not pip) throws error related to SSL

[imagejan]

When I try running hatch build on a newly created project, I get the following error:

$ hatch build
WARNING: pip is configured with locations that require TLS/SSL, however the ssl module in Python is not available.
WARNING: Retrying (Retry(total=4, connect=None, read=None, redirect=None, status=None)) after connection broken by 'SSLError("Can't connect to HTTPS URL because the SSL module is not available.")': /simple/hatchling/
WARNING: Retrying (Retry(total=3, connect=None, read=None, redirect=None, status=None)) after connection broken by 'SSLError("Can't connect to HTTPS URL because the SSL module is not available.")': /simple/hatchling/
WARNING: Retrying (Retry(total=2, connect=None, read=None, redirect=None, status=None)) after connection broken by 'SSLError("Can't connect to HTTPS URL because the SSL module is not available.")': /simple/hatchling/
WARNING: Retrying (Retry(total=1, connect=None, read=None, redirect=None, status=None)) after connection broken by 'SSLError("Can't connect to HTTPS URL because the SSL module is not available.")': /simple/hatchling/
WARNING: Retrying (Retry(total=0, connect=None, read=None, redirect=None, status=None)) after connection broken by 'SSLError("Can't connect to HTTPS URL because the SSL module is not available.")': /simple/hatchling/
ERROR: Could not find a version that satisfies the requirement hatchling (from versions: none)
ERROR: No matching distribution found for hatchling

I try running on Windows 10, and I tried both Git Bash and Anaconda Prompt.

And I don't know if that's relevant here: my computer is configured using a proxy via HTTPS_PROXY environment variable, which works fine when directly running pip or conda.

Any ideas anyone?