KDE connect is a collection of software to make your smartphone connect to your KDE desktop (it also works with Windows and probably Mac OS, but this is not the subject of this article).
With these software, you can:
Although KDE connect is very good, it performs its magic via network packets, thus with WIFI (it would work with LAN I guess, but I don't know any phone with a Ethernet port). WIFI advantages are the ubiquity and the high transfer rate, but it's also a huge battery consumer. It also requires your phone to be connected to the same network as your computer which isn't always possible (like if your computer does not use its WIFI connection or if you have a office network connection where your smartphone isn't allowed to connect).
You can set a wireless access point on your phone (usually made to allow your computer to share your smartphone's Internet connection) but that means powering up both WIFI and your LTE modem for a local (non internet communication).
If you don't need utterly fast communication with your smartphone (understand, if you can stand that transferring a photo takes few seconds), using WIFI is not required and you can use Bluetooth instead. KDE connect android and desktop source code have a "bluetooth" path, but they are disabled by default (you need to compile them to have them enabled). I did this but there was no config whatsoever to add the connection. Also, the Bluetooth path is not fully functional from what I understood from the developer's comments.
If you need this build, just ask I can send you the APK.
The solution I'm describing below involves using BlueZ to start a network connection over Bluetooth. Once the network connection is set up, you simply need to tell KDE connect on your phone to connect to the computer's assigned IP address, and you're done.
On the computer
On the smartphone
Install KDE connect from F-Droid (or step 0: Install F-Droid). Before launching KDE connect, you'll need to provide some authorizations (depending on your phone, it might ask you by itself, but it didn't on mine). So you'll need to navigate to your Android's Settings screen and type "Authorization" in the search box. Then select the KDE connect application and allow it to access the phone (sorry no screenshot here)
Go to your phone's settings and type "share" in the search box. Then select "Via Bluetooth" page to allow sharing your connection via Bluetooth.
In your notification tray, click on the Bluetooth icon, and select "Connect"
Then accept the connection on the phone (you might need to go to the Bluetooth setting page first).
In your notification tray, click on the network icon, then the Bluetooth icon and select "Connect"
Once it's connected, use the right rectangle to display the details of the connection (you need the IPv4 address):
Start KDE connect on your phone, and click the submenu button on the top right, and "Add a device by IP". You'll need to enter the IP address you've seen on the network page.
If all goes well, your computer name will appear on the device list on your phone. Click on the icon, and select "Associate". Click "Accept" on the computer and you're done.
In the smartphone, you'll need to authorize all the features once it has correctly connected. Just follow the instructions displayed on your phone and you're done!