That looks really nice! Is that pretty common to do?

Yes, quite common. Many people do it for the reason you have. Other people do it because they have a tile backsplash and don't want the tile grout behind the range to get splattered from cooking and be an extra cleaning chore. Other people do it because they like the look.

Google "stainless steel backsplash behind range" or "stainless steel backsplash behind cooktop" and then click on the Google Images tab and you will see a lot of pics.

30x24

https://www.lowes.com/pd/Broan-Duct-Free-Universal-Backsplash-Plate-Stainless-Steel/1092009

36x24

https://www.lowes.com/pd/Broan-Duct-Free-Universal-Backsplash-Plate-Stainless-Steel/1092003

In answer to your question --- are these common? --- yes, as Shannon says, they are common. There actually can be two possible issues when replacing your current range with a slide in. One is what is discussed above, which covering the vertical gap in countertop backsplash that used to be filled by your free-standing range's built-in backsplash. The other can be horizontal gaps when your new range's top isn't butting flat against the steel plate on the back wall. (This can be caused by all sorts of things including an uneven back wall or just the design of the range -- some slide-ins have bump outs in the lower back of the range which result in the stove stop sitting forward of the wall.) You can buy trim pieces to cover the gaps at the top either as an accessory if offered by your stove's maker or from a company like MicroTrim. You might prefer a bolt-on pro-style backguard vent riser. Those used to be only for premium-priced pro-style stoves but even the likes of Samsung now seem to offer versions for their slide-in ranges. While helping a friend, I recently ran across these examples on a Home Depot page. Also, IIRC, I'm pretty sure some big box or hardware stores stock off-the-shelf backsplash plates with an inch-or-two-wide lip across the bottom edge. That can cover horizontal gaps at the back of a slide-in range going against a wall as yours will and you might only need to buy and install one piece..

you all are wonderful! I had no idea about any of this.