[Resolved] File.vue and style lang="scss" shows errors, in *.scss as well.
Answered
scss not recognized in *.vue or *.scss files, even after scss plugin installations

If I format a file CTRL+SHIFT+F it's breaking apart $ and variable name as well:

There is no SCSS file association possible after plugin install:

Plugins:

And if scss file associated with CSS:

IntelliJ IDEA 2018.1.1 (Ultimate Edition)
Build #IU-181.4445.20, built on April 2, 2018
Licensed to Yevgen Golubenko
Subscription is active until June 1, 2018
JRE: 1.8.0_112-release-287-b2 amd64
JVM: OpenJDK 64-Bit Server VM by JetBrains s.r.o
Linux 4.4.0-119-generic
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Apparently I had to enable SASS Support in order for SCSS files/syntax to be recognized. Perhaps renaming this into SASS/SCSS Support would be a better thing to do as it's not clear that SASS means SCSS as well...
You need to make sure that Sass support plugin is enabled in Settings | Plugins, and `*.scss` extension is assigned to SCSS file type in Settings | Editor | File Types