As for Ardour itself, it is clearly completely open source [1].
https://git.ardour.org/ardour/ardour/src/branch/master/COPYI...
Ardour is free software (and therefore open source). Ardour is not proprietary software.
Ardour is a commercial product. They sell pre-built binaries, updates (perhaps some level of guarantee/support for those binaries?) etc. Ardour is not "freeware", shareware or a hobby project or anything else like that.
1. Commerce is bad and somehow at odds with free software and the GPL,
2. The only way to do any kind of software trade is proprietary software.
In fact, commerce is beautiful and a cornerstone of economics and our civilisation. Most people in the free software community are not opposed to commerce. What they are opposed to is proprietary software. That is, claiming ownership of software and therefore doing commerce based mostly on rent-seeking and retaining power over said users. Free software and the GPL aims to disable this, but it does not disable, nor does it oppose, commercial software, unless you believe (2), which is evidently false, as you can see with Ardour.
Now that said, I do support avoiding language that is offensive to people even if it doesn't seem to me like it should be (so long as it's still clear what is being communicated. I don't like Orwellian expressions).
[1] https://ubuntustudio.org/2022/11/ardour-7-1-backports-availa...
[2] https://packages.debian.org/search?keywords=ardour
[3] https://packages.fedoraproject.org/pkgs/ardour7/ardour7/
Ardour is licensed under GPLv2.
Show me where to pay for the pre-built product:
https://community.ardour.org/download?platform=linux&archite...
All I see is a direct download link. If you want to pay that's optional.
""" Subscribe
$1, $4, $10 or $50 per month ... """
""" Single Payment
If you choose to pay less than US$45 ... """
""" Free/Demo Version
Periodically goes silent after 10 minutes.
No access to nightly (development) builds. """
And, if you wonder, you can't enter 0 for the payment.