There is “Host information” screen that shows number of albums, songs, movies etc. but it seems that information there is outdated. Could you please provide an option to reload information by request or load it each time the dialog opens or reload it once in some period of time.
The data is real time with Yatse info.
To update your yatse cache just browse the sections in yatse 
I am in the process of digitizing of my CD collection. In between I listen to music and watch TV series using Yatse as remote (browsing sections?). I wanted to see how many albums I already processed and Yatse shows 45 while I already have more than 200. It seems that 45 it is the number of albums that was present when I first started using Yatse recently.
One last thing that I tried is to switch in the “Media Centers” to “Local device” (however there is nothing on my phone) and then back to the Kodi that I use in hope that information will be refreshed but nothing happened.
Are you sure you scanned the media in Kodi first? Pretty sure that’s your issue here.
You can use the custom command to force it from Yatse. https://kodi.wiki/view/Update_Music_Library
By browsing I mean list the songs inside Yatse in library mode, when in any music library view you can also swipe down to force a sync. But Yatse only displays what Kodi sends.
OK, got you. Of course the library was scanned and I was able to see all my albums in the Kodi. I am a new user of Yatse and thought that the left drawer menu items do same thing as the buttons on top - just navigate in the Kodi. Now I learned a new functionality and after I entered the Music Library locally the album count was updated. Thank you.
Well explore more then it’s all faster to use Yatse directly then the remote screen