Memos is self hostable and is "cross platform" by nature of being web-based only. There is a 3rd party mobile app MoeMemos but it doesn't add anything special over the quite excellent progressive web app for plain Memos. Of course you can't use it offline since it's web-based. But I have an always on VPN connection between my phone and my server so home so it's fine.

Notesnook is recently open source, but as of yet not self hostable. It is on the roadmap though. This one is privacy/security oriented and has native apps for just about everything as well as a web interface.

Quillpad is the closest interface-wise to Keep, but it can only sync with Nextcloud and I can't run that beast on my old hardware. Too clunky and slow.

I've been on this hunt for awhile but I realized that I use Keep differently than other folks on the same journey. It's mostly a list focused service for me. Sometimes with check boxes, sometimes not. Most of the FOSS not taking apps can use some markdown, but that is a bear to use on mobile without a quick way to inject a checkbox. Memos has a button for a few formatting items on each "post" and thankfully one is the Markdown checkbox shortcut.

For notes, personal knowledge management, and everything else I use and love Obsidian.