No SAGA available in QGIS Processing
I had faced a similar issue but resolved it with saga install. You need to install proper version of SAGA. I installed saga via apt install. SAGA version in Ubuntu 18.04.3 repository work very well with QGIS 3.10
sudo apt install saga
Please confirm that saga_cmd is installed and you get following output
Restart QGIS [3.10 in my case] and you should see SAGA installed as shown below.
In QGIS 3.4, the SAGA provider is already a core plugin. Therefore, you can also change the SagaAlgorithmProvider.py file directly, by:
sudo nano /usr/share/qgis/python/plugins/processing/algs/saga/SagaAlgorithmProvider.py
then change the REQUIRED VERSION from 2.3. to 7.3.
This worked for me.
One solution (and far from optimal) working for me is to install Processing from SAGA Nextgen Provider.
At the time this SAGA next gen plugin works only with SAGA 7.2 and won't launch in QGIS if SAGA is the newest version (7.3). But when you unzip the plugin, change the version form '7.2' to '7.3' in provider.py and then reinstall the plugin it works with SAGA 7.3 as well.
I couldn't find a better solution and I haven't tested if everything works (but at least the functions I need are there and working).