With your minimal requirements, a Raspberry rumning stock Rasbian or Armbian, and SSH/SCP commands (and an Android/iPhone SSH/SCP client) could do the trick.

The disadvantages to this approach is you'll have to learn the commands you need for every use case. The advantage to this approach is you'll have to learn the commands you need for every use case, and we would learn a lot of useful stuff.

Source: I used a Pi for this need, before I bought a fancy Network Attached Storage (NAS) device.

Edit: Further pro/con:

• It'll work with almost everything. SSH and SCP are very old and stable and there's tons of apps.
• Too many options. I had to pick my clients a bit at random, and research and switch to find what I wanted. Even my first random choices did work fine though.
• None of the SCP apps for phones have particularly nice interfaces, in my opinion. This is a minimalist solution, and it feels like one.
• Nothing proprietary - no one is going to Google-kill this solution due to lack of profits.
• All the software you need for this is free.
• This solution can be extended in tons of nice little ways later. I.e. something like AWS CLI for trivial off-site back-up to a secured S3 bucket.
• A well chosen NAS gives all of this functionality, and much more, but for a lot more money.