Comparison between se.fit for predict_merMod and lme4's predict.merMod

[AlpDYel]

As the users might know, for a long time lme4 did not have standard errors for predictions and users that needed such standard errors required to do them by hand or use functions that did it for them for external packages, such as the predict_merMod.

Since 2023, lme4 now has standard error for predictions, albeit they are labeled as experimental. I was wondering if there was any attempts to go over the lme4s standard errors and predict_merMod's standard errors and compare them?

I am planning on going over some basic results with a toy dataset when I get a chance to do so but I wanted to see if there are results available already