As an iOS + Linux user, icloud.com has been helpful. Access to reminders, notes, in theory messages (I don't use it so can't vouch for it).
The thing to do is to use Chrome (yes...), and open the page. In the hamburger, go to "Create a Desktop shortcut". Choose "open in a new window". This gives you a desktop shortcut to open the page in a standalone way. Visible to your launcher, distinct ctrl+tab... it's janky but I've found this works well.
Firefox please add the Chrome standalone desktop shortcut feature!
Yeah, I also tend to bring up iCloud Notes in a browser tab. It’s still far from perfect, since Notes is usually an offline-first app, which you miss out on here.
I’ve been looking for a replacement, but nothing really gives you
I have been using Joplin for longer notes, which provides good sync, offline-first, and good platform support. It's Janky but for writing out post drafts the sync has been super good for me. It lets me finish typing out a thing on my phone in a pinch, no futzing around with roam necessary.
For tiny notes I've been using.... facebook messenger chat to myself. Say what you will about Meta, at least their stuff mostly works.
I still feel for you. I really want to commission some software that feels good to use on Linux ("feels good" in the real sense, not in the GNOME sense)