And why is this illustration of a man with a pineapple (ananas) on his
chest found with the definition of toffee-nosed? Does it imply
anything about language?
I believe I have found the connection between the pineapple on the man's shirt and toffee-nosed, in the end, the easiest explanation was the most logical. In Victorian England, and elsewhere in Europe, the pineapple fruit was a symbol of wealth and great status. Nowadays a pineapple costs £1.72 in British money, but in 1862 it sold for 5s - the equivalent of £149 in real terms.
The illustration is therefore a caricature, the ascot tie has taken on the semblance of a pineapple, and by doing so the illustrator is telling us about the man's social position, class and wealth.
Pineapple cultivation in Britain
Its introduction to Europe resulted in a veritable mania for growing
pineapples and parading them at the dinner table became a fashion
requisite of 18th century nobility. In Britain and the Netherlands the
practice was not the preserve of the aristocracy but also extended to
the gentry. The pineapple was a representation of owners’ wealth but
also a testimony to their gardeners’ skill and experience. Producing a
crop of tropical fruit in the colder climes of Europe before the
advent of the hot water heating system in 1816 was a remarkable
achievement and was, perhaps not unjustly, described as ‘artistry’.
The founding of horticultural societies during the Victorian period
brought new opportunities for the display of pineapples at
horticultural shows, a tradition that lasted until the beginning of
the 20th century. However, the inevitable demise of the pineapple as
horticultural status symbol began with the arrival of imported fruit
from the Azores at the end of the 19th century.
Sources: BBC Business, Building Conservation and Pinterest
Notes on 19th and early 20th century men fashion
The gentleman in the image appears to be wearing an imperial collar, a very high (3-inch) stiff, standing detachable collar. This style was known as an Imperial "lap-front" or "poke" collar. Clicking on the link will lead you to a photo of a young man, you'll notice that he isn't wearing a jabot but instead an ascot tie, the typical accompaniment for that type of collar, which became a popular combination from the 1880s and was usually worn with men's morning dress.
Basically, the illustration was chosen to illustrate toffee nosed because the man is evidently wealthy; appears to be hoity-toity; snotty; snooty; uppish; and has the airs of a proper toff. He personifies the image of the clichèd British upper-classes before the end of the First World War.
The only thing I found which could possibly connect the gentleman's elegant attire with this exotic fruit was this Australian idiom:
Oxford Dictionaries says
The rough end of the pineapple A situation in which someone receives unfair or harsh treatment
Example: The workers, so far from being emancipated, would continue to get the rough end of the pineapple, as they had from the beginning of time.