I didn't find any methods at api.limesurvey.org/classes/remotecontrol_handle.html to get LS's version. Is there a way to do it other than scrapping the HTML page once logged ?

Create your own remote function : extensions.sondages.pro/development-and-...i/documentation.html

Thank you but I was looking for something more, let's say "built in" and reliable enough when applying future upgrades of LS.

Then : no way currently …

If you need it :
1 : create a feature requets
2 : make a pull request
3. wait …