Hi Alexander Kulikov
Would you mind sharing your whole project with us?
The build.gradle file looks to be mixing androidx dependencies and legacy support dependencies, this may be causing the issue you are seeing. You've also included some dependencies that will be transitively included by the toolkit.
Let's try and get the build.gradle file dependencies in order first before we chase down the issue.
Unless you need to make changes to the toolkit, you don't need to include it as a local module like so:
implementation project(path: ':arcgis-android-toolkit-100.6.0')
What I would recommend is removing that line and adding the following:
implementation "com.esri.arcgisruntime:arcgis-android-toolkit:100.6.0"
Please also see the Toolkit Repo for instructions of how to use the components: GitHub - Esri/arcgis-runtime-toolkit-android: ArcGIS Runtime SDK for Android Toolkit
Luke