EDIT

This simulation isn't about ROCAUC, but it does show that there can be a significant difference despite overlapping confidence intervals.

set.seed(2023)
N1 <- 10
N2 <- N1
alpha <- 0.05
R <- 10000
reject_with_ci_overlap <- rep(0, R)
for (i in 1:R){
  
  # Simulate data
  #
  x1 <- rnorm(N1, 0, 1)
  x2 <- rnorm(N2, 0.5, 1)

  # Set trackers of conditions being met
  #
  tracker_overlap <- 0
  tracker_psignif <- 0
  
  # Determine confidence intervals for each mean
  #
  ci1 <- t.test(x1, conf.level = 1 - alpha)$conf.int
  ci2 <- t.test(x2, conf.level = 1 - alpha)$conf.int
  
  # Check if the confidence intervals overlap
  #
  if (
    ci1[2] <= ci2[2] # Is the upper limit of ci2 above the upper limit of ci1?
    & 
    ci1[2] >= ci2[1] # Is the upper limit of ci1 above the lower limit of ci2?
    ){
    tracker_overlap <- tracker_overlap + 1 # Then there is overlap
  }
  if (
    ci2[2] <= ci1[2] # Is the upper limit of ci1 above the upper limit of ci2?
    & 
    ci2[2] >= ci1[1] # Is the upper limit of ci2 above the lower limit of ci1?
    ){
    tracker_overlap <- tracker_overlap + 1 # Then there is overlap
  }
  
  # Check if the two-sample t-test p-value is below alpha
  #
  if (t.test(x1, x2, var.equal = F)$p.value <= alpha){
    tracker_psignif <- 1
  }
  
  # Check if both conditions are met; if so, put a 1 in place i 
  # of reject_with_ci_overlap
  #
  if (tracker_overlap > 0 & tracker_psignif > 0){
    reject_with_ci_overlap[i] <- 1
  }
  
  # Print progress
  #
  if (i %% 1000 == 0 | i < 5){
    print(paste(
      round(i/R*100, 2), "% complete",
      sep = ""
    ))
  }
}

# Calculate the percentage of iterations where confidence intervals overlap
# yet the two-sample test rejects the null
#
mean(reject_with_ci_overlap) * 100 # 14.19%

I get this behavior in $14.19\%$ of the iterations, so this is far from unusual.