I really think that it is very easy to find romanticism characteristics in every poem, especially in the ones which are closely related to this time of history.
First of all the main characteristic of romanticism that we can find in those sonnets is nature. For example it is represented in the first sonnet with the following sentence:
“Hold like rich garners the full ripen'd grain;”
That sentence makes me think that nature is so important that it will always be the essential element of romantic poems, because nature is so full of feelings and interpretations that the reader can go beyond those simples words and focus on what they really want to mean.
The second sonnet also set nature as an important element of romanticism, but also it is combined with another element that really called my attention; death. For instance, the next part of the sonnet incorporates both, nature and death:
“My spirit is too weak; mortality
Weighs heavily on me like unwilling sleep,
And each imagined pinnacle and steep
Of godlike hardship tells me I must die
Like a sick eagle looking at the sky.”
I think that the theme which is closest to Keats’s lived experience is death and intelligence. He during his life was really close to death and poorness, so that is why his sonnets are related to that. Besides he studied medicine, which I think is the main aspect why he incorporates the brain, pain and books.