Where did the phrase "bury the carnival" come from?
The burial of the Carnival is a mock funeral enacted in many countries in Europe and Latin America at the end of Carnival, either on Fat Tuesday or Ash Wednesday. It appears to have evolved from a pre-Christian ritual linked to the celebration of the end of winter and renewal of life. Here’s a passage from a 1919 paper (my bodface in all quotes):
When performed on Shrove Tuesday or Ash Wednesday, the ceremony of the expulsion of Death or Winter was pretty generally known as the Burial of the Carnival (Shrove Tuesday) in Germany as well as in France, Spain and other countries of Europe. But the names of Death, Winter and Carnival seem to cover an ancient tree-spirit or spirit of vegetation.
(Maximilian J. Rudwin, “The Origin of the German Carnival Comedy,” Journal of English and Germanic Philology, Vol,. 18, No. 3, July 1919, pp. 402-54.)
The earliest references I found to it in English are from 1842 and 1845:
This burying of holidays is a general practice. Traces of this custom are yet to be met in some of our villages. They meet in Northamptonshire, "to bury the wake ;” and though this phrase merely means to finish it up with a good drinking bout, it is a sufficient testimony to the old Saxon custom once existing there. They [the Germans] bury the carnival, fast-nacht, or Shrove-tide, in the same way. (William Howitt, Rural and Domestic Life of Germany, 1842.)
The Carnival of Barcelona is the most amusing of Spain, then the Rambla is a masquerade out of doors, while Thursday, “Dijous gras,” is celebrated gastronomically. On the first day of Lent, Barcelona goes out of town into the country to “bury the Carnival,” “enterrar ál carnesioltas.” (A Hand-Book for Travellers in Spain, London, 1845.)
And here’s another reference from 1851. But here the burial of the carnival marks the end of mi-carême (French Wikipedia), a carnival-type festivity in mid-Lent:
There will be two grand balls this evening […] And last, not the least, the grand Masquerade Ball at the Academy of Music, which will be the rendez-vous of all those who are fond of fun and pleasure. All Paris will go there and bury the carnival in the best style.
(The New York Herald, April 12, 1851.)
The OED (paywalled) has a couple of definitions of bury that may be relevant (but no "bury the carnival" that I found):
b. fig. To consign to oblivion, put out of the way, abandon and forget. c. To consign to a position of obscurity, inaccessibility, or inaction; often refl. and pass.
However, what may be going on here is that you're seeing, in the quotations you posted, translations from another language which have the force of the OED definitions quoted above. I don't think that language is German (I didn't find anything on the German Wikipedia website, although that may be my inadequacies in the language), but it might be Russian, where I can't make a judgment (although Russian has a "carnival" cognate).
Basically "burying the carnival" is eradicating the last traces of the revelry and getting ready for the austerity of Lent, as @Josh notes.