Hi Owen,
> When I search for "download bitcoin core" my top result is bitcoin.org, which is out of date and doesn't have 22.0
This is an issue related to SEO which only website owners can fix or maybe others can help who know better.
> It seems confusing to have two sites that seemingly both represent bitcoin core.
There is only one website which represents Bitcoin Core full node implementation. You can download Bitcoin Core from https://bitcoincore.org
Ensure that you are using the correct domain as some people have registered domains which use punycode, looks similar and spreading malware: https://bitcoin.stackexchange.com/a/107738/
> Maybe the download links could be removed from bitcoin.org and instead it could just link to bitcoincore.org?
You can open an issue in website repository: https://github.com/bitcoin-dot-org/bitcoin.org and tag Cobra who owns the website and domain.
Alternately you could also try a derivative of Bitcoin Core: https://bitcoinknots.org/ maintained by Luke Dashjr.
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Prayank
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