I am not seeing the word “widow” on the baptism record.
Just says “base child of Elizabeth Wooton”
In the case of James in 1815, "Widow" is written in the "Quality, Trade or Profession" box.
The earlier baptisms of Thomas in 1805 and Nancy Eastmond in 1811 both have "base child of Eliz. Wotton" and do not include "widow".
A possible interpretation is that her husband was absent at the time of the first two, but by 1815 it was known - or assumed - that he was dead. That would certainly be consistent with him being a soldier serving abroad during the Napoleonic War.
A second name like "Eastmond" for an illegitimate child is
almost always an indication of an alleged father - but of course James needn't have the same father.
If Thomas Nichol was his father though, then it quite likely he would have used that surname, and put Thomas on his marriage registration.
David