All 4 Uses

nevertheless
in
The Overcoat, by Gogol
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Either because he had met with a thing utterly unknown, but for which every one cherishes, nevertheless, some sort of feeling; or else he thought, like many officials, as follows: "Well, those French!†

nevertheless = despite that (used to connect contrasting ideas)
Others were shut, but, nevertheless, showed a streak of light the whole length of the door-crack, indicating that they were not yet free of company, and that probably some domestics, male and female, were finishing their stories and conversations whilst leaving their masters in complete ignorance as to their whereabouts.†
*
Nevertheless, he ordered that the official should be kept waiting, in order to show his friend, a man who had not been in the service for a long time, but had lived at home in the country, how long officials had to wait in his ante-room.†
A being who bore meekly the jibes of the department, and went to his grave without having done one unusual deed, but to whom, nevertheless, at the close of his life appeared a bright visitant in the form of a cloak, which momentarily cheered his poor life, and upon whom, thereafter, an intolerable misfortune descended, just as it descends upon the mighty of this world!†

Definitions:

(1) (nevertheless)
despite that

Based on idea 1 we might not expect idea 2, but this is a way of saying that even though idea 1 was just stated, we still have idea 2. Synonyms include in spite of that, despite that, nevertheless, nonetheless, on the other hand, in contrast and but.
(2) (meaning too rare to warrant focus)