AirPort Extreme question

My Apple AirPort Extreme is old but still working

What model of AirPort Extreme do you have? If the AirPort Extreme is tall shaped, like a tower about 8' tall......then tell us that you have the "tower" version.

If the AirPort Extreme is flat shaped.....like a small white pizza box.......look on the bottom of the device for the model number on a label, or it might be embedded in the foam pad base. The model number starts with an "A" followed by four numbers. Post back that info.

it is now recommended by spectrum that I upgrade to there advanced WiFi router so that I can get a static web address for my solar panel inverter.

You don't need a new router to get a static Internet web address.....you need to ask your provider if there is an extra charge for this type of service since other types of "workarounds" are really complicated, and will probably require an IT person to set things up. I'm not sure if Apple still even supports this. Example:

https://www.dynu.com/DynamicDNS/IPUpdateClient/Apple-Airport

However, if the AirPort Extreme 6-7 years old or older, then it might be time to think about switching to a newer router with higher speed capability and higher security features.

if I do that what happens to all the files on my router hard drive ?

Confused a bit on this, since an AirPort Extreme does not have a built in hard drive. Are you saying that you have a USB hard drive attached to the USB port on the AirPort Extreme.......or.......maybe you meant to say that you really have a Time Capsule, which does have a built in hard drive?

is the idea that this is all unnecessary thanks to iCloud backup

No, since iCloud does not back up the entire contents of your Mac. So, if you purchased a new Mac and you want to transfer the backup of the old Mac over to the new Mac.......to make the new Mac look just like your old Mac.....you won't be able to do this.

The whole idea with Time Machine backups is that if the hard drive on your Mac fails, and you get a new drive installed on the Mac, you can transfer all of the data in a Time Machine backup over to the Mac with the new hard drive.......so your Mac will look the same as it did before the hard drive failed.

Or, as mentioned previously, if you buy a new Mac and you want the new Mac to look just like your old Mac, you can transfer the data from a Time Machine backup of the old Mac over to the new Mac, so it will the same as the old Mac.