I do believe balenaSound will handle what you’ve installed and provide you with a pleasurable listening experience throughout your home. I use balenaSound throughout my home and I love it!
For each room, you will need to purchase a Raspberry Pi, an SD card (recommended: Sandisk Extreme 8GB or larger) an amplifier module for the RPi, a good quality power supply and some misc hardware. There are a number of companies who make amps that can attach to a Raspberry Pi. Consult the balenaSound docs for suggestions . You don’t need the same hardware for each room. You can use smaller (cheaper!) RPi boards for rooms that don’t accept audio input, e.g, they are clients, but not servers. The docs explain those differences .
Once you have some hardware in-hand, follow the directions to set up your balena account and install balenaSound  onto the SD cards, assemble, connect one of the devices to a set of test speakers, and try using the system to see how it works for you. If you want to spend the least amount on a test, get yourself just a Raspberry Pi 4 with USB power cord and SD card, and an aux cable, install the SD card, and connect the aux cable between the RPi and another device, like a boombox that has an aux input. Then send some music to it from your phone or iTunes. That will get your feet wet, and you should be able to decide from there whether you’re interested in investing in more hardware to fill in the rooms. Note, the headphone jack on the RPi does not have very good audio quality. So don’t let that discourage you. Using an amp that attaches to the RPi can render nearly audiophile quality.