First of all, thank you all for replying and trying to help, I appreciate it.
So short update:
Today I took all the stuff I have been keeping in my spare room to fight reverb and put it in my living room as you can see in the attached photo (just for testing).
There's much less echo now and it improved the sound.
I feel like putting the rug closer to the speakers and getting the table out of the place were the most significant changes.
I think I can hear more bass now which makes me feel like the sound is more full.
Another interesting discovery - I use the TV as the source (or the amp's Bluetooth) and it turns out the volume of recordings in the Apple Music application on the TV is significantly lower than the iPhone's application. That's super weird. So now I just airplay from the iPhone to the TV or using the Bluetooth of the amp directly.
I also realized that prior to a few hours ago, I had a 'sound check' setting on the iPhone that might have messed with the tonality, IDK.
Although I recall that I couldn't tell the difference between streaming from iPhone or using the native app in the TV prior to today (their volume happened to be similar because of that volume limit setting that was enabled).
I do have something like 5 days to return the amp if I want.
Now I wonder if should just EQ the system to my liking (after acoustically treating the room) or replace the amp, maybe with a tube one or Arcam SA20.
My options are quite limited where I live.
The thing I liked about this amp is that its price is very competitive here. Some products from other places of the world can cost double the price for absolutely no reason.
So I will further test that amp but I am still wondering if I should just replace it or EQ.
Why?
One of the best sounds I've heard is coming from my Apple Airpods pro 2nd gen with applied audiogram. That sound I've tried to obtain in my HiFi system by DIrac Live and an abundance of different house curves. I'm so close now that I have settled to a curve with small 1 dB differences here and there in the slope.
@Pawnshop123
These KEFs are bright "ab standard" as various users have pointed out. You probably are used to the boosted 60-70 Hz from the soundbar at the same time, exaggerating the impression of the bright KEFs. Give it some time and see if you get used to them or use EQ to taste. Easy as that.
You are right. In the soundbar, I have 'woofer setting' and it was all the way up (but frankly, I don't hear THAT much difference when it has a 'neutral' woofer setting).
And yes, I love the sound of the Airpods Pro.