What speakers for amp and Receiver

You really need to decide to value surround or 2 channel.  Most here will easlly say 2 channel, and in my opinion sounds better even with movies.

But you can do both.  Generally, advice here will only be about the 2 channel.  If your receiver has home theater bypass, (it should), you then send preamp outputs to a better 2 channel amplifier of your choice, and then with speaker wires to your main L and R speakers.  this conceivably gives you the best of both worlds, with multi channel amps and  processing going to all the surround stuff, and dedicated 2 channel available to listen to through a better amp, best speakers, and no processing in stereo or direct mode.  Now the Integra (or any surround receiver) will still be the weak link, but at least minimized.

The most important thing is calibration on a home theater. It is very likely that is not correct. There should be a profound improvement in the sound. I would not let them  off the hook until it sounds awesome. What is hooked to what and how is important with a distribution amp. That should not be powering your main fronts, 

Also, if this stuff is all new... then breakin can be important. Run the stuff round the clock for a while, 

Unless you experience jaw dropping improvement in sound., Get your money back. This stuff while not high end should be immersive and dynamic... awesome. 

For details. Put your question in ChatGPT or some other AI. 
 

It does need to breakin period but should sound good now focal is a great product. It needs dsp like anthem,marantz,denon all have build in dsp in thier avr. I have the marantz av 10 with 16 channels and some mismatch speakers but it all had dsp done sounds great.  Denon av 1 is on sale 5k and is fantastic as well 150 watts 15 Chantelle. Your dealer should have a dsp system. Have them do it .until then play the system on about 25 % volumn to break the system in 24 hours a day for several days. Good luck.

Did the OP even demo this gear in person?  If not, how did you know you would like the sound of this gear combo before you bought it?

Before Saturday, I would disconnect all the speakers except for the left and right main, with those two at the 60 deg isosceles triangle setup to the center listening position and at least 1 foot from the side and front walls.  With all video sources off and the Integra in stereo mode with no room correction, I would play / stream some intimate jazz trio (bass, piano, drum) like Dr. Billy Taylor or similar and just listen.  How does it sound?  Is there 3 distinct sound sources in front of you with a nice soundstage?  If not, you might need more room tuning like a large carpet on the floor, drapes on any decent sized window, etc., before going with major room tuning investments.  If it does sound nice, maybe you are overpowering / complicating the room with all your additional speakers, starting with the center channel.  Once you get it dialed in more with just the two channel, maybe connect the sub and try to find the best location for it (probably not in the center between the two mains / not under the center channel speaker).

Audio and AV setup is usually best if it is done incrementally, I think...

You got a 9.2 receiver and a 7.4.1 Atmos configuration. So your installer sold you a 4 channel add-on amp to power the speakers unaccounted for by your receiver.  That means you have 2 unused channels of power. That’s all I see wrong with what you were sold…but if it sounds little better than a Bose Lifestyle system, something is amiss. Incorrect setup and calibration or an extremely adverse acoustic environment are possibilities. Let them spend some more time dialing it in before you decide. The gear is certainly capable of producing very good performance.