there were a couple things that added at the same time, and it's caused some confusion. Matter and the new architecture are 2 different things. Sadly your older Mac won't be able to access either one, since they've been added only in the the new releases
Matter is a new protocol, it's basically just a language. it just specifies how devices should talk to each other and format commands. it's available for anyone to use, unlike apple's proprietary homekit. Previously, you'd look at the box and see the homekit badge, and know that device would work with homekit, chances are that box also had Alexa and google home badges also, meaning you could use them with any of those three controllers. With matter, if you see a matter badge, it means it will work with all 3, as well as any other controllers that also support matter. It makes things easier for manufacturers, and hopefully cheaper for us, since they only have to code in one control protocol, and be able to work with many different controllers, as opposed to 3 separate sets of code to talk to apple, Alexa, and google.
The new architecture rearranges the basics of how the home app works in the background. In the old architecture, all that apple stored was a device list (and scenes and such). Each of your phones or Macs would load that list and then act independently, So when you launched home on your phone, it would grab the list, your phone would then reach out to each device, or bridge in case of things like hue, to get it's current status. When you launched home on your Mac, it would do the same thing, even if you had just launched home on the phone.
With the new architecture, one of your home hubs will become the leader, it handles all of the communication to devices. So one of your homepods/aTVs will consistently keep tabs on your home devices. When you launch home on your phone, your phone reaches out to that HomePod, and gets the status of every device from there. I'm not 100% sure if commands from the phone go through that hub or directly to the devices. (away from home they obviously all go through the hub)
--The new architecture update takes place on your apple devices
--the matter upgrade takes place on your devices (bulbs and such). Your phone will just talk either matter or homekit deepening on how the device talks to it. And Alexa will just speak either Alexa or matter.
you can do one or both of the updates
for matter you can update some of your devices and not others. The others will continue to work as they always have, the ones you update will just speak matter
Personally, I'm holding off on changing anything to matter, as I have no real need. Its main selling point is wider control options, but everything I have is already working in homekit. Plus, I've seen many people not having smooth change overs, and manufacturers are still working the bugs out. If what you have is already doing everything you need it to, matter is not necessary at this time. But if you were to buy something new, you could get a matter version, and know that it would work with both apple and Alexa out of the box.
not 100% sure on this one also, but I believe that changing to matter makes it a new device, so you loose all scenes and automations you've got set up. You will also loose adaptive lighting going to matter, as that's a homekit feature.
The new architecture can make the home app a little faster to respond, but it sounds like you're not doing too much in the actual home app, so even that might not be necessary for you.