Not an app, and I haven't really used it, but tinylist feels quite Google Keepy. You can add it to your home screen, but it doesn't seem to work offline.
I absolutely second this, if you aren't worried about built-in syncing (I use Syncthing to solve this, also cool piece of software), and if you really like the idea of Markdown/text-only notes with image/file attachments, there is absolutely no better tool. Plus, if you think you can get value out of the note linking feature, you can make some incredibly detailed knowledge bases. Really powerful tool when you need it to be, dead simple note-taking by default, it's a damn good app
Trilium Notes, Logseq, or Obsidian.md if you're looking for something more advanced.
Self-host something like bookstack, docuwiki, mediawiki, or wikijs for something more.... permanent? I wouldn't really use these to jot something down real quick but I do put a lot of finalized? notes in a wikijs docker image I host.
Obsidian.md. It runs on markdown files, so even if you decide you don't like Obsidian, you've still got all the files. It's super easy to sync with SyncThing or probably Google Drive or whatever. It's free, and the are a ton of plugins for it. Peri sure there's a Lemmy community for it around, too.
One option is Notally on F-droid and on the Google Play Store. It's FOSS (Free and Open Source Software) and it has all of the features you mentioned. I use it as my everyday note taking app and I have zero complaints so far.
There's Safe Notes on F-Droid as well, which is pretty much identical to Notally feature-wise, but your notes are encrypted (locally).
Do you send messages to yourself? Is this a thing you can do? I never tried. That would be pretty cool.
edit: um... yeah. create an empty room with just yourself in it. Now I feel silly.
I've always used ColorNote. It does have several advanced features but they're all optional. It's been updated for 5 years now and basically hasn't changed. Still free, no ads, easy to use. A rare exception on the Play Store. Whole app only 4Mb.
I'm a big fan of a small app called UpNote. It's clean and simple with a few power features you can use if you really dig into it. It largely has the same baseline set of features as Obsidian, but it supports syncing across devices out of the box and has a one-time purchase of a lifetime membership.
Great, now how about a sketching app that follows all the same criteria that OP mentioned. Something for quick and dirty sketches. Nothing fancy. One that can do sketches and notes would be even better.