However in general it’s better for the side with less space to exchange pieces (much less than this position). The logic is simple. If your bishops don’t have a long range they are just big pawns, they are not worth 3 pawns. Or if your rooks in the middle game have not much maneuvering spaces then they are just fat pawns not worth 5 pawns. So it is extremely beneficial to exchange it with your opponent pieces as they are more valuable than yours. Also when you exchange pieces, automatically you free new squares for your remaining pieces thus you have a better maneuvering options.
Why does the trade of pieces benefit the side with less space?
However in general it’s better for the side with less space to exchange pieces (much less than this position). The logic is simple. If your bishops don’t have a long range they are just big pawns, they are not worth 3 pawns. Or if your rooks in the middle game have not much maneuvering spaces then they are just fat pawns not worth 5 pawns. So it is extremely beneficial to exchange it with your opponent pieces as they are more valuable than yours. Also when you exchange pieces, automatically you free new squares for your remaining pieces thus you have a better maneuvering options.

The player with less space will find it more difficult to develop as there less open squares and lines on their side of the board. They will also have trouble maneuvering to neutralize the opponent's threats and get counterplay. Trading a couple of pieces helps relieve the congestion.

There is a very good example of this made by GM Supi
With less space, it's ok to have fewer pieces.
Like in a bus, if you have some people, it's fine.
But when you have a huge amount of material to keep in a really closed space, it gets out of control, you need to open it up. Like a bus with an overflow of people
I have a very general question - why does trading off of pieces in the centre aid the side which has less of a space advantage? Here is an example to illustrate this point - I came across the following commentary about a certain position:
'' Black is happy with a massive exchange of pieces on e4; that’s the first thing to know. The trade of pieces would benefit black who has less space, therefore we (white) should avoid it and white has three reasonable options: 8.Ned2, which aims to recycle the knight via c4, the second option, 8.Neg5, puts some pressure on f7/e6. This would force black to make some concessions in his development. Third ... is 8.Ng3, which is the most popular and the preference at the highest level.''