I picked day one up as a journaling app many years ago, and have enjoyed it. But I've now mostly left the apple ecosystem and I'm ready for a new solution. An important feature to me is the calendar view that both shows you what days you have entries for and allows you to see previous year's entries on a day. The lack of this feature knocks out the most recommended alternatives on this community (joplin, obsidian, and logseq come to mind). Journey cloud and diarium are strong picks, but I'd prefer non proprietary and stronger self hosting support. Along with better platform availability. Memoria is also in consideration, but the documentation is pretty light and it's hard to tell if it will function in the way I expect. Likewise with memos, which I've seen suggested on here.
Needs:
Usable on linux (I can live with a web app)
Calendar view showing days with entries
Encryption
Cloud sync functionality (no local only apps like rednotebook)
Nice to haves:
Proper app for linux, android, ios
Ability to import a day one backup, preserving my 5 or so years of journal history
FOSS
Selfhostable
Support for media (primarily photos)
Prompts for password on every launch
Equivalent to "on this day" feature allowing you to view previous entries on a day
That's where I found my current top contenders. Nothing had exactly what I'm looking for, which is why I turned here. It probably just doesn't exist, but doesn't hurt to ask.
You can sync Obsidian with your own storage location. There are plugins to do a lot of what you're asking for. Downside is that it's not open source, though your content is all stored in plaintext so you won't lose it due to lock-in. It also might be more than your asking for and a simpler, more tailored, solution may be out there. Paired with a self hosted Nextcloud server, you may solve a bunch of your PIM needs at once.
If I suggested helix + dvalv on your desktop, Markor + Valv on your phone, and SyncThing for syncing... would that be sufficient? It's basically what I use, but without the dvalv/Valv component because my notes are never hosted outside of my phone or desktop, so I don't need the encryption.
The missing piece would be a "calendar view"; I'd have to think about that one. Myself, my entries are named by ISO 8601, so sorting by timestamp or name both work. But if you want a traditional grid calendar with, like, colored days for the days with entries, that'd require another program.
It sounds to be, though, that you've set up your requirements such that you really just want a web app, with client-side encryption. I'm old enough to have learned the value of application-independent data storage; SQLite is about a complex as I'm comfortably with, and flat files in a directory are even better.
This is something I've been thinking of developing myself as I'm looking for a new project to start and I don't like any of the journaling options available right now, foss or otherwise.
I'll look into Day One to see what kind of features I'd need to replicate/have alternatives for and see if it's something I want to dive into, especially because my journaling needs are very simple so my initial plan was to make something very simple.
You could approach it as a Joplin plugins. I switched from Trello to Joplin Kanban and now Joplin YesYouKan. Seeing how powerful they can be, upping Joplin's journaling game should be doable! And you don't have to even start your whole own new project.