It depends upon the depth of the back cushions, and what the inside seating depth is. Compare the new 38" with the current 42" you have with regards to inside seating depth and see what the difference is.

My vintage sofas are around 32" but they have thin backs and down filled back cushions that flatten a bit so they provide good seating depth despite their overall shallow depth.

I, like a lot of people, dislike a sofa or chair that is 'too' deep. You have to either slean (sit and lean back), or else one's legs would stick straight out.

I'd suggest you measuring the actual seating area, from the front of the bottom cushion, back to the front of the back cushion with it compressed a bit. The actual sitting depth on my sofa is just 22" but it is very comfortable, and I think of it as my "perfect sleeper".

New sofa would have rolled arms though so already a bigger presence.
Imho, rolled arms are a waste of space, particularly in a smaller area, and it is often uncomfortable to reach a beverage or something on an end table.

Maybe you should continue to look?

Will you be using an end table or two and lamps?

Do you have a picture of the new sofa?

What is really important is the seating depth as well as how it fits in the room. The average sofa is 20" to 22" deep but an older sofa that started this way will measure deeper as the back cushions do flatten after a period of time.

Even if it has loose back cushions, 38" deep should be plenty. The one in the picture that you posted looks like it would be about 37" deep.

Lars