All 4 Uses

nevertheless
in
Leaves of Grass
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You will hardly know who I am or what I mean,
But I shall be good health to you nevertheless,
And filter and fibre your blood.†
Chpt 3 *

nevertheless = despite that (used to connect contrasting ideas)
I see those who in any land have died for the good cause,
The seed is spare, nevertheless the crop shall never run out,
(Mind you O foreign kings, O priests, the crop shall never run out.)†
Chpt 12
The sign is reversing, the orb is enclosed,
The ring is circled, the journey is done,
The box-lid is but perceptibly open'd, nevertheless the perfume
pours copiously out of the whole box.†
Chpt 18
Nevertheless, be ready, be not weary of watching,
He will soon return, his messengers come anon.
A Hand-Mirror
Hold it up sternly—see this it sends back, (who is it?†
Chpt 20

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)