Spoiler: No. People feed their snakes in different enclosures for two reasons. The main concern is that a snake will go into "feeding mode" when you open and reach into their usual enclosure if they are fed in that same space. Then, once the enclosure's open, they may bite you after mistaking you for prey. For this reason, people suggest that you move your snake to another enclosure before feedings so they don't associate their usual home with food every time the enclosure's opened.
There are many issues with the argument above. Firstly, there has yet to be any real evidence that snakes become more aggressive for food when fed in their usual enclosure. Secondly, if a snake is going to become more aggressive in the enclosure they are fed in, they would bite you when you're going in to move it back to their normal enclosure.
The other issue is you should not handle snakes after feeding because you risk them vomiting up the food since they lose some of their defense when a large meal is inside them. Vomiting or regurgitating a meal is not only a waste of a mouse or rat, but is also very dangerous and uncomfortable to the snake. If you decide to keep the snake in the second enclosure for a few days until it had time to digest, they will have to stay in an inaccurate setup for a few days which can put more stress on them, causing more issues. You could choose to create a whole second proper enclosure just for feeding, but that would be expensive to purchase all of the supplies, complicated to keep both enclosures heated and properly humidified, and on top of that, it won't even matter because the snake would develop that "food aggression" in the second enclosure (which doesn't exist to begin with).
The second concern is the snake can potentially ingest some of their substrate if their mouse or rat comes in contact with it.
Although this can be a concern with some substrates, you're going to be just fine with a snake ingesting the occasional wood chip or other digestible substrates. Check the videos below for good and bad choices in substrates.
Watch the video below for more information!