It's a fair bit of work to set up, but I replaced Keep with Obsidian.
I suppose you could just pay for obsidian sync and then basically have parity. I do not. I use syncthing to sync my notebooks (vaults in obsidian terms) between my devices.
To get my existing notes, I used Google Takeout to get a copy of all my data, but you can just ask for the Keep data. They'll send you a bunch of json files, which I was able to extract the text of my notes from pretty easily and copy into Obsidian notes.
When I think of notes, I think of little one off Post-It's I can quickly reference at a glance later. Then throw away once I don't kneed it later. But all the "Notes" apps out there aren't about replacing notes, but instead are all about replacing notebooks. They're WAY overkill, and far too much work for such a simple use.
That does look like what I'd want.
The one time I tried to setup something In docker on my home NAS I failed pretty hard. But this looks promising enough to try again.
When HedgeDoc 2.0 comes out, it will have an "Explore Page" which is the last missing piece to pretty much have feature parity with keep. That said, it's a long way out.
When I was using Android tablet and phone, Quillpad is what I used. Very similar layout to Keep. It doesn't have sync built-in but does have markdown. I used to export a note and sync with Syncthing.
When I switch my tablet for a Linux laptop I had to find something else. Notesnook is what I went with. The layout is more of a list of notes v Keep's twin columns, has sync in the free version (works great) and markdown.