Add analyzer similar to Resharper's "Method can be made static"

Please add analyzer similar to Resharper's "Method can be made static".
There is Microsoft analyzer CA1822 but it will show warning even for methods that aren't private.

Start by reviewing the existing analyzer structure and Microsoft analyzer CA1822, which the issue cites as the closest reference. Determine the intended private-method scope and how similar analyzers are tested; done means the new analyzer identifies applicable methods without reporting the broader cases that CA1822 warns about.

Written by the indexing model from the issue text.