Some of these elements can be discovered in places like the Caeremoniale Episcoporum -- the book of ceremonial for prelates -- for it is frequently also found to be the case that the higher up the proverbial ecclesiastical food chain one would go, the more retention one would find of these customs.
Something that many people note about the papal chapels, conclaves and other solemn liturgical events in the Vatican of yesteryear was the use of green carpeting spread throughout the choir/sanctuary. This can be seen in images taken from the Sistine Chapel as well as St. Peter's Basilica.
Lest one be tempted to think this is just a case of colourized photos, it also shows up in paintings:
Not to mention illuminations from the 15th-16th century:
Some might be tempted to think that this was purely an accidental or purely arbitary stylistic choice on the part of the Vatican, but what many many not be familiar with is that these colours were actually prescribed in the liturgical tradition, and if you were to look closely through some the sacristies of Rome, you'd no doubt yet still find a number of green rugs and carpets, though only the most traditional of churches can now be found to still use them, such as can be seen here at the usus antiquior parish of Ss. Trinita dei Pellegrini in Rome:
.".. all the floor of the sanctuary, up to the lowest step of the altar, ought to be suitably covered with a green textile [panni]." (C.E. I, xii, 10)"...all the lower steps of the altar [should] be covered with a large and beautiful carpet [tapete] that, as far as possible, they may be more conspicuous than the rest of the sanctuary, which is covered with green cloth [pannus]. If such a carpet be not available, let the footpace at least, which is nearest the altar, be covered with some carpet." (C.E. I, xii, 16)
Why green? A good question. Within the context of the Caeremoniale Episcoporum one can be forgiven for wondering if it has something to do with the fact that the traditional colour associated with bishops is green as seen in the colour of the galero found on bishops coats of arms and traditionally also in the colour of the band or tassel of the cappello Romano of a bishop or archbishop:
Similarly, traditionally when a prie-dieu is placed within a sanctuary, it was covered in drapery that related to the rank of the prelate: red for cardinals and green drapery for other prelates:The history of the use of green as the colour of the episcopacy is, according to Nainfa, as follows:The prelates of the Roman Court wore purple clothes as members of the Pope's household, long before any bishop thought of habitually dressing in that color. The councils of the middle ages, legislating upon ecclesiastical dress, prescribed a dark color (pullus color) for the cassocks of priests and other lower clergy, reserving undetermined bright colors for the use of dignataries. In accordance with these decrees, bishops, before the sixteenth century, generally dressed in green, for the simple reason that, before the modern progress of chemistry, the green dye was the best and most easily obtainable... the marked prevalence of green caused this color to be regarded as the episcopal color, and so it has remained to this day. (Costumes of Prelates of the Catholic Church, p. 204-2-5)
Nainfa continues within this section noting how this would shift toward the purple that we now all know due to the importation of goods from the orient, no doubt in imitation of the papal court. He continues:
... the Ceremonial of Bishops [Caeremoniale Episcoporum], while prescribing purple as the proper color for the bishop's dress, did not abolish the established tradition of using green as the distinctive episcopal color; nay, it confirmed it by ordaining that green should be the color of the principal token of the episcopal dignity -- the pontifical hat. Roman usage, in accordance with this accepted tradition, and the known mind of the compilers of the Caeremoniale Episcoporum, has always emphasized the principle that green is the habitual color of the drapery on the bishop's throne and prie-dieu, of the canopy over his coat of arms in the hall of his house, when he rides in state, and of the cushion which, before 1870, was carried by a valet for the bishop to kneel on in the not infrequent case when he would meet on the streets of Rome a priest carrying the Blessed Sacrament to the sick. (p. 205-206)
For the sake of thoroughness, and in case any sacristans might be looking to implement this tradition, I would note that during times of mourning and penance, green is substituted for purple in the case of the drapery for the prie-dieu and throne. Similarly, on solemnities when the bishop himself offficiates from the throne, these draperies taken on the colour of the vestments of the day.
Returning then to the question of "why green carpets?", the question remains whether this has anything to do with this association. The issue, however, is that unlike other uses of green described above, this usage goes beyond liturgical circumstances in which a prelate is present, and so in that regard, this would seem to speak against there being any "prelatial association." Still, it might be possible that this was something that was originally indeed so associated, having been utilized mainly in prelatial contexts and then finally extended to the broader liturgical custom of the Latin church (much like the purple of the papal livery would also come to be so extended) but for the moment, this is purely speculative.