Does the basket's 3 enter the Level 579 queue?

No. It is a fixed number printed on the picture basket and never appears as an active tray group.

What are the last visible Level 579 fragments?

A black square near the upper-left and two small white/gray clusters near the upper-right remain before the empty board.

Food Hunt: Pixel Puzzle level guide

hard 11 colors

Drain the active cyan 60/80, green 54/50, and white 58 opening row, ignore the basket's fixed 3, and reserve capacity for the balloon tail.

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At the first playable frame, note active cyan 60, green 54, white 58, cyan 80, and green 50; do not add those five values again as fresh nests.
Wait for the first lane to release, then admit the actually exposed fresh white 60, cyan 66, white 20, or white 40 group.
Let the cyan/green/white families remove the grass, cloud, and child layers while keeping one lane for the red shirt, yellow garment, and small balloon colors.
As the basket and balloon cluster separate, feed brown, gray, white, red, orange, yellow, purple, and magenta groups in their displayed counts, waiting whenever a long cyan or green remainder is active.
At the late row—brown 13, magenta 2, black 3, red 1, pink 1, with white 10 waiting—let each small remainder leave before admitting the next white group.
Wait for the last black square near the upper-left and the two white/gray clusters near the upper-right to leave; all five slots then show empty.

Colors in this level:

Cyan, Green, White, Red, Yellow, Orange, Purple, Brown, Gray, Magenta, Black

Treating the starting active 60/54/58/80/50 row as five fresh taps and overfilling the tray.
Counting the wooden basket's fixed 3 as a nest or move budget.
Adding another large cyan or white group while the late red 1, pink 1, or black 3 remainder still occupies a lane.

Board notes 5 details

Layout: A red-haired child in a red top and yellow lower garment stands in green grass beneath a cyan sky, with purple/orange/yellow balloons and a brown basket marked with a fixed 3.
Goal: Let the five starting trays remove the grass, child, sky, basket, balloons, and isolated outline pixels until the board is empty.
Opening: The first playable active row reads cyan 60, green 54, white 58, cyan 80, and green 50; fresh queue values below it begin white 60, cyan 66, white 20, and white 40.
Danger Zone: Repeated cyan/green/white groups fill all five lanes while small red, yellow, purple, orange, brown, and gray balloon or outline details wait.
Mechanics: All five slots are open at the start; the wooden basket's 3 is static picture art, and the late board leaves a black square plus two white/gray clusters.

Does the basket's 3 enter the Level 579 queue?
No. It is a fixed number printed on the picture basket and never appears as an active tray group.
What are the last visible Level 579 fragments?
A black square near the upper-left and two small white/gray clusters near the upper-right remain before the empty board.