Bit of a technophobe here
Does anyone know of a solution, short of getting a new phone?
Unfortunately, because of the first statement, the second is pretty much an impossibility. Your phone has the latest OS Motorola released for it. Is it the most recent OS SOMEONE has put on it? Probably not, but doing that is not without its pitfalls. You'll either need to become less of a technophobe pretty quick or reconsider the aversion to replacing the device.
The OS installed on a device is built for THAT device. The device manufacturer is responsible for developing and releasing the OS for their devices. Just because a newer version of Android is out does not mean that any particular device will get it, this is due to either the manufacturer of the processor (or SoC) in the phone not officially supporting that OS on that hardware or because the device manufacturer has decided not to continue support for the device.
Google is also dropping support for older versions of Android on a regular basis. The most recent drop was either Ice Cream Sandwich or JellyBean, leaving your device precipitously on the edge of that cut-off as well.
App developers can choose to have their minimum-supported OS even newer than Google's minimum-supported OS, and even block authentication on older versions of their app to force you to update. What this means is that even if you find a version of the app that will work on your device, it may not actually work. I have a couple apps on my phone that block log-ins from older app versions, even if it's a saved log in, and I'm on Pie (the latest OS)!
Even if you DID learn how to install a custom ROM on your phone (the only way you'll get a newer OS), it's simply a band-aid and you will be constantly "chasing" that lowest-supported version. Not to mention that while it's possible to do the results may well be undesirable performance-wise since that phone was released in 2013.
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