I think one of the great things about classical music is it includes so many sizes and types of ensembles you can find pieces suitable for any use or occasion. Pretty much all classical has a wider dynamic range (SPL difference between the loudest and softest passages) than typical pop music. However, a lot of chamber music (for anywhere from 2 to 9 instruments) and works for string orchestra (self-explanatory) or chamber orchestra (about 1/3 as many players as a large symphony orchestra) has a moderate dynamic range suitable for background listening, if that's what you're looking for. The "strength" of the contribution of different instrument groups is also important in determining dynamic range: music dominated by woodwinds and strings with little or no brass + percussion tends to have lower range.
On ... the ... other ... hand ...
, some of the greatest music for full symphony orchestra was written with large to extreme dynamic range, including passages with "all out" playing by brass and/or percussion instruments clearly intended to be heard at high volume, because the loud parts are essential to what the composer was trying to express. If you're not familiar with musical notation, you should know that there are distinctive marks in classical music to indicate five levels of "soft" starting with "very very very soft, barely audible" indicated by ppppp (in musical Italian that's "pianissississississimo") then pppp, ppp, pp, and finally just p, meaning moderately soft. On the loud side we've got f, ff, fff, and ffff ("fortissississimo"). There's no fffff, perhaps because classical music lovers should have the chance to hear MORE THAN ONE loud piece, if you get my meaning. (Hearing loss is a serious concern for members of large orchestras - many musicians nowadays use hearing protection. More surprisingly, violinists who play exclusively in small ensembles can suffer occupational hearing loss - that's because the violin is held close to the player's ear, and contrary to the belief of some, the human ear is most susceptible to damage from high frequencies 1 to 5 kHz, not bass.)
I'm betting the readers of this thread would like an example of the high dynamic range side of classical music. I've chosen the Symphony No 4 in C minor by Dmitri Shostakovich, in a 2014 performance by the Royal Concertgebouw Orchestra led by Andris Nelsons. This conductor recently recorded a complete set of Shostakovich symphonies (1 through 15) with the Boston Symphony. Keep in mind that extremes of contrast, not just the loud parts, are essential to the musical expression, listen carefully to what happens in the quiet passages too. Both audio and video quality are high (considering it's Youtube), so watching the musicians is enjoyable.