what you could do is copy the entire content of the E drive to the new Samsung 1 tb SSD drive, which we will assume for argument sake you have named X drive having used “compmgmt.msc” to format etc the new Samsung 1 tb SSD drive and give it the X drive letter.
once that is done using compmgmt.msc you will unassign the E letter from the old drive and for example assign it the letter Z, you will then unassign the X letter from the Samsung 1 tb SSD drive and give it the E letter.
thus the Samsung 1 tb SSD drive will ultimately replace the old E drive and become E itself, you can then give whatever drive letter you then prefer to the old drive.
or
that is assuming the standard way of moving a steam game from one Steam Library folder to another Steam Library folder on another drive doesn’t work - which is just dome by clicking the properties for the given game in the steam application (click on the game, select properties, local files, move install folder)
it really depend what else is on your currant E drive and must that stay as E.
I cloned msfs to a new m.2 SSD using Macrium Reflect (free). Because of DRM I had to run a repair afterwards, but it only took a few minutes and everything has run perfectly since and I’ve wiped the original drive to use for other things.
I would recommend using a build-in SSD, but if your USB connector is new (version 3.2), you could probably get away with running it from an external drive.
If not, go for an internal SSD, because of transfer speed concerns.