Please pull one of those wall connections off and take a photo. Upload a 'large' one if you can so we can see details.
The key here: If they ran cat-5e and a speaker wire to EACH ROOM, then you are in a lot of luck.
My standard wiring, as a custom installer, TODAY, is a cat-6 wire to each wall plate location and a 4 conductor 14-gauge speaker cable to the ceiling speakers.
Which appears to be EXACTLY what you have.
No way would I do a ton of Sonos units. But, you could. You would need a Sonos Amp for each room. That's $650 for EACH ROOM.
Or, you get one Sonos Port, and a HTD Whole House system for $1,500 with built in phone control. The HTD system allows you to swap the existing keypads as long as there is a cat cable run to them, which it looks like there is.
You can certainly hire a company. If you're in the Washington DC area, give me a call... (shameless plug for me), or you can call a local company that does this work. But, sites like you are at will help out. I do this for a living and do offer advice for those who are willing to get their hands dirty and buy a few tools and spend some time watching YouTube videos. It is a new skill for many. But, there are also guys out there who will just take care of this for you.
Trust me, they will use your existing infrastructure. On the other hand, a proper installer will go through and certify that each cable is good and that it is in the proper location and labeled accurately before they hook up brand new gear. I literally just finished a home. The final bill was about $8,000 for a 16-zone system. All cabling has been fully tested and a brand new equipment rack has been installed with shelving, Sonos, amplification, and distribution with phone control. So, not a inexpensive system and about half (well, less actually) of that $8,000 is labor. About 60 hours of work went into making sure everything was perfect.