| take on sth: | to begin to have a particular quality or appearance; to assume sth |
| take sb on: | to employ sb; to engage sb to accept sb as one’s opponent in a game, contest or conflict |
| take sb/sth on: | to decide to do sth; to allow sth/sb to enter e.g. a bus, plane or ship; to take sth/sb on board |
In the third paragraph, “take on” is used in the sense:
“to begin to have a particular quality or appearance; to assume something.”
This matches the dictionary entry “take on sth: to begin to have a particular quality or appearance; to assume sth.”