refactor content scripts to make it easier to implement Thunderbird support

[tomholub]

One thing I noticed is that the content_scripts/webmail folder already on master is quite disorganised and not so easy to work on to add Thunderbird (or any other webmail) support. I country try and refactor it a little bit myself, and that could make it easier for you.

Originally posted by @tomholub in #5690 (comment)

[tomholub]

Additionally, there used to be automatic code style changes on save (for example ordering of private/public methods). Was it disabled, does it work for anyone else?

[sosnovsky]

Additionally, there used to be automatic code style changes on save (for example ordering of private/public methods). Was it disabled, does it work for anyone else?

private/public members ordering were auto-fixable in TSLint, but it needs to be manually fixed in ESLint.
Other common code styles issues are still automatically fixed on save.

[tomholub]

Got it 👌