An apt description of Romanticism is that of a "journey" from the corruption of society and the limits of rational thought toward the freedom of the spirit and imagination and the truth and integrity of nature.
"Thanatopsis," (a title which combines two Greek words, thanatos =death and opsis=seeing), is a lovely meditative poem replete with beautifully vivid images. The verses of this poem describe the journey of death, but not a death as the end of something; rather, it is as a continuum that allows the deceased to become one with Nature. For, after having "lost each human trace" and one's individuality to the world, the one who has died will
...mix forever with the elements,
To be a brother to the insensible rock....
Old Ocean's gray and melancholy waste--
Are but the solemn decorations all
Of the great tomb of man.
It is, then, to that sublime (that which inspires awe) level of communion with Nature that man who is interned in the earth, lying along with kings and patriarchs, will rise to mix with the elements, "surrendering up/[his] individual being," establishing a relationship with other human souls and with God, becoming what Emerson named the Over-Soul.
I would say that it is a good example of Romanticism for all three of the reasons given above (and also some other reasons as well). Romantics were very concerned with emotion as opposed to reason. They were also interested in "the sublime" -- stuff that fill us with awe and fright and wonder all at the same time. The supernatural and death do that. So all of the things you mention are Romantic ideas. And all are present in Thanatopsis, which is, after all, concerned explicitly with death (which arouses emotions and is connected to the supernatural).
I would also say that Thanatopsis fits with Romantic ideas of loving nature and feeling that humans are a part of nature. Bryant tries to comfort us with the idea that death will just make us be part of nature.
So Thanatopsis is clearly a romantic poem for all of these reasons.