To get things going here and also because I'm interested in what kind of fun stuff you're running on your phones, I'll post a list of apps that I'm using daily or that are part of my Android experience.
To start it all off, I'd like to emphasize that I try to run FOSS apps almost exclusively and I also don't use Google Play Services whatsoever (not even MicroG). I do run some very few closed source applications in a separate profile with Insular, but I plain out refuse to run them if they flat out require Google Play Services.
Feel free to tell me what YOU are running in the comments!
My installed Apps
AdAway | Blocks ads by utilizing root access or by acting as a local VPN**
Aegis | Provides 2-factor authentication codes, includes a repository of icons for your services
Aurora Services | Required for background installations with Aurora Store****
Infinity for Reddit | Feature-rich Reddit client (future uncertain due to Reddit's API-pocalypse, however, you can compile Infinity with your own API, as described here)
Insular | Creates a separate (work) profile where you can install "big brother" apps**
Noice | Create and play back profiles of overlapping noises to drown out environmental noises (use version 1.3.3, version 2.x requires internet access and an optional subscription)
SlimSocial for Facebook | Wrapper for Facebook's website, so you can interact with people that refuse to use any kind of messenger, but are still present on Facebook
SuperFreezZ | Freeze applications that you're not using***
Open Camera | Feature rich camera with Camera API v2 support, usually the best FOSS camera on 3rd party ROMs
*CAN be used as a client for self-hosted services
**Offers additional features if root access is present
***Requires root access to be present
****Part of a Magisk module
Edit: Added some links and changed Infinity's description
I use Syncthing and KDE Connect both. They're fantastic at what they do- wireless sync specific folders between devices, send/receive files, share a clipboard between devices, remotely operate a device, share notifications etc. Basically you can create your own seamless ecosystem of devices that belong to any platform! If you're like me and use a lot of offline-only apps, these two will let you sync your data between 2 or more devices. I use it for my offline music library (fully legal of course, no question about it haha lol), logseq notes, books (again, definitely completely legal).
I also use BitWarden, but I might switch to Keypass because it is fully offline.
Does syncing a password vault or app settings work flawlessly like that or do hiccups occur? I usually try to use things that are FOSS and offer a selfhosted backend, but I'm not opposed to the usage of fully offline applications, as well.