Non-Apple wifi router?

I don't know how much, if any, kind of channel configuration you can do on all those devices. The problem is, in reality there's only 3 clear wi-fi channels and that's not much room for the proliferation of everything you and all your neighbors have running. I used to use a wireless ISP and everything was okay until a few years ago when everything went wireless nuts and all my neighbors crowded me off the ISP with streaming Netflix etc. Streaming is particularly bad because it means constant traffic vs. just everything sharing the same channels at different times. You may be your own worse enemy in this.

I’ve been running an AirPort Extreme 802.11n (4th Generation) for quite a while (obviously)

A 4th Gen AirPort Extreme is going to be at least 7 years old and as much as almost 9 depending on when it was originally placed into service.....while the average useful life of a router designed for home use is about 5 years.

That doesn't necessarily mean that the product will fail at an average 5 years, it means that is the point where the performance has already been heading downhill for a year or more, and it will decline at a fast rate as it ages. So, if the AirPort were 5 years old, it might be broadcasting a signal at 75-80% of the power that it was when it was only 2 or 3. An 8 or 9 year old AirPort might be operating at only 40-50% at this point.

Would the Netgear or Linksys be a better bet?

Virtually any new router would be a better bet at this point, but there are never any guarantees. Check with the store before you buy to make sure that you can return the new product for full credit in case things don't work out as well as expected. The reason.....you cannot know how well a new product will work in your home until you try it out in your home.

Personally, Netgear products have always worked very well for me, so between a Netgear or Linksys router, I would try the Netgear first. But, another user might have a totally opposite opinion.

If you are interested in one of the newer "mesh" wireless systems, Apple is now selling the Linksys Velop system for sale.

How has the Netgear behaved with your Apple devices?

I haven't used a Netgear router in the past, but the other Netgear products that I've used.....including a wireless security system called Arlo.....have been flawless.

As mentioned I'm hoping devices don't keep dropping off the network and having to re-pair.

As I mentioned above, the bottom line is that you will not know how well a product will perform in your home until you try it out in your home. That's why I recommended that you have a clear understanding of the store's return policy before you buy. An XYZ router might do a great job for your neighbor, but not for you. That is the nature of the beast with wireless.

I've also heard that Apple disbanded the division that develops wireless routers 1.5 years ago.

You will always "hear" a lot of things, but Apple has made no official announcement about anything like this and they continue to sell their AirPort routers in the stores and online. There was also a recent firmware update for the AirPort routers, so it's hard to believe that this would have come from a division that had been disbanded.

The current products are in need of a refresh though, since they were introduced almost 4 years ago.

Personally, I 've used the current model AirPort Extreme 802.11ac for the past few years and it has done very well. It covers a 2500 square foot home easily. If you want to stay with Apple, you might give this model a try.....but, as I said, it is getting "a bit long in the tooth".

"Mesh" is the latest and greatest wireless technology. I doubt that Apple will go this way though, since they are currently offering a Linksys "mesh" system for sale in their stores and online.