I'm so glad that you were able to identify the problem through testing, given your current problem, data updates can only be achieved by manipulating the refresh of a single data set .
The virtual network (VNet) data gateway is currently a Preview feature, and may not be as perfect as it could be in the parallel refresh section. From the available documentation, it seems that there is no refresh related introduction.
By the time this feature is officially rolled out, the problems you're experiencing should be fixed. Let's all look forward to it!