It depends heavily on what the starting point looks like. For that you need to measure with a measurement mic and Room EQ Wizard, Sonarworks Reference ID (buggy, don't recommend) or the IK ARC stuff.
In my previous apartment where for aesthetic reasons the only "room treatment" was things like bookshelves, rugs etc. There was a huge boost around 130 Hz, and some smaller issues in other frequencies. Using room correction via Sonarworks helped with that a lot.
In my current apartment the room where my Genelec M040 (similar size to the 8040) studio monitors are is surprisingly more neutral. Sonarworks correction didn't do a whole lot here, the little EQ switches on the back of my Genelecs were enough.
For headphones, correction can be beneficial. My Beyerdynamic DT990 Pros have excessive highs, so correction works well to counter that. I use them as my "everyday listening" headphones because they are very comfortable. The Sennheiser HD6XX I use with my Axe-Fx 3 are far more flat out of the box so correction has only small effects.
Proper room treatment will always be better but software or even EQ correction can help reduce or remove the most glaring issues.
i have exactly that issue in my current room , there's a huge boost around 130hz (i think in part due to the big desk i have) , and there's some dips below 100hz , i ended up using REW and using EQ to fix that issue , it's a small cube style room with windows as well which doesn't help,
i always leave the door open too, otherwise that build up is even worse
i also mix/produce retrowave style electronic music, so adding a bit of room treatment definitely helped as well, but the huge resonance from the desk, is still the main issue, which is what EQ is correcting for , i'd say it definitely helps in dialing in tones for playing out live etc..
and it also makes a really nice bit of difference to the overall listening experience of music etc..in said room
if money is a concern, REW software is free, you can buy a measuring mic for under 50 euros (i use a Behringer ECM8000) just need a stand to go with it, and then you can apply EQ via your DAW and if you like with EQO for system wide
Julian Krause made a really good video on how to do it, in case anyone is interested