Maybe you can also explain why Standard Notes doesn’t meet your needs so we have more information?
For the site recommendations, Joplin does have an in-built collaboration feature if you choose to host the notebook with them or self-host their server software (See Sharing a notebook with Joplin Cloud | Joplin). I’m not certain, but I do suspect that you would need to individually pay for two subscriptions to their service to be able to make use of this (one for you, one for your partner).
For off-site recommendations, Obsidian has shared vaults, if you’re willing to pay for two subscriptions as well to their official sync service. Obsidian is closed-source, but the sync service is end-to-end encrypted, and they claim that they don’t collect telemetry at all. For what it’s worth, I haven’t seen anything that casts doubt on them here.
It also stores your notes purely as plain markdown in a folder of your choosing, so as another commenter said, you could avoid paying for their subscription service and just set up an external syncing solution like Syncthing.
Lastly, I will say that if you’re okay with sharing all your notes with your partner, then you can just share an account with them. You’d be able to use Standard Notes or Notesnook this way (also works with Obsidian and Joplin). There is the caveat that you can’t edit notes at the same time, but I’m not sure if the official collaboration features of Obsidian and Joplin can handle that either.