This is one approach to adjusting the label and quantity sizes and providing a "margin".

Check out the documentation under plot.euler for other formatting options.

As eulerr is based on grid you can provide margins in effect by adjusting the size of the viewport used for plotting. The answer shows a plot reduced to 80% of the original height and width.

Although I noticed that the relative positions of the venn diagram elements changes as you rerun the code I never found that the circles straying outside the canvas margin.

set.seed() did not seem to change anything.

library(eulerr)
library(grid)

my_dt <- data.frame(
  value = c(1:8), 
  A = c(TRUE,  TRUE, FALSE, TRUE,  TRUE, FALSE, FALSE, TRUE),
  B = c(TRUE,  FALSE,  TRUE, TRUE, FALSE, FALSE, TRUE,  TRUE),
  C = c(FALSE, FALSE, FALSE, FALSE, TRUE,  TRUE,  TRUE, FALSE)
)

p <- plot(euler(my_dt[, c("A", "B", "C")]), 
     quantities = list(cex = 2),
     labels = list(cex = 2))

# edit the viewport dimensions

p$vp$width <- unit(0.8, "npc")
p$vp$height <- unit(0.8, "npc")


p

^{Created on 2023-06-30 with reprex v2.0.2}