If you want the TL;DR; plugging a USB drive into your router should make it available to other devices without the PC on. Hard to say how the various mobile devices will access it though. They may not all support the routers file sharing method. Testing with a cheap USB may be a good first try. If you want to know how to solve this for a more advanced/complicated home network, keep reading.
I am in the information security field, so take my setup like you would some of these mustang build threads. It may be a bit more than what you want to commit to, but its an idea of how to solve the
problem, and probably some you don't have.
I have a Synology external drive array/network attached storage. My unit has 4 drive bays, but you can also get a dual drive bay version. The box is basically a little bigger than a stack of 4 disks. I can plug it in anywhere on my network (my house is wired with cat6 cable, so I have wall jacks in most rooms). However big or small your network is, it just needs a port on it somewhere. This is effectively the next step up from a USB external drive attached to a router.
- It is it's own device. It runs a version of Linux and has a web console to manage it. No other device is required to manage it other than something with a web browser. It doesn't matter what you use for your primary computer. You don't need to know anything about Linux to use it.
- It can manage redundancy for drive failure or speed. You can configure it for mirroring drives, or more complicated RAID solutions. It does this very easily.
- You can replace drives without shutting it off. They are hot swapable.
- It can run a variety of apps, including a full blown backup solution (not just a scheduled file copy), or PLEX media server. It has an app to mirror cloud storage like OneDrive or Google Drive as well.
- It has a variety of networking methods for connecting to various file systems.
- It's more expensive than a single USB.
How I use it:
- Run the Synology backup software and schedule a backup of my important folders to a mirrored drive.
- File share for photos so other machines can all access them
- Plex server for watching movies from my Roku on my TV. I don't have a DVD player by my TV.
- Mirror my OneDrive to Plex. My phone pushes all pictures to OneDrive. I can look at my pictures on my TV without doing anything, seconds after I take them. When I travel, my wife can see pictures on a big screen without me sending them or posting them on social media. My remote family can also see my pictures through the Plex app and my giving them access explicitly.
- A place to store my MP3 music.
With a couple Western Digital Red drives in this device, I have confidence in my decade + of family photos and CD/DVD/BluRay media content not disappearing. To avoid ransomware, I still need to be smart with how I access the content. For example, connecting to a remote share, most ransomware will still encrypt it. It won't get access to backups through backup software. If I access my media through a media server like Plex, it also wont get access to that.
A Synology box is like dropping in a crate motor. It's not as complicated as trying to put a fox motor in, but it's not as easy as just tuning your existing motor either. On the other side, there are a lot of benefits to having new tech with more options to work with, if you can use those features. It's also a significant upgrade from having no motor
Sorry, that was REALLY long winded. Hope it helps more than it hurts.