You use the settings to point the new installation to your models folder on the e drive.
But if you look at the data folder on the e drive, I would expect that it does not have the same "date last updated" as the model folder - it should be older because the system will still use the data folder on the c:drive.
Once you have changed the settings to point to the models on e drive, then click the rebuild collection button - this will then rebuild the data folder on the c:drive.
I have just tested this myself to make sure it works 😊