VueJs plugin for the site, css class is overridden, how to be?

Question

material design

Good afternoon everyone.
Is this a continuation of the question Packaging Angular or Vue into a single file for use on a third party site?
This is how things stand at the moment.
The plugin is written, everything works fine, but there is BUT. I have used VueCli3, VuetifyJs and its components.
When I transfer all packaged components to a third party site. my plugin's styles are moving out.
From the documentation, I thought that VueCli3 would build all the styles and JS into several files, and so on. it's all inside the template then no styles will be affected.
Can someone tell me what to do next or how to properly build the project so that the styles do not move out.