Piotr, the case you described it is typical for SDL Trados Studio projects settings and also for verification plugins, because Studio is project-based tool. For example Number Verifier works in such way. However, my approach is different. LanguageTool should work even for projects/packages created on Studio without my plugin installed.
Please set your desired settings (in any project) and save them as user defaults (Save As User Defaults). These settings will be stored in Windows settings and will be applied always when Studio project don’t contain LanguageTool Plugin settings.