iMac loses internet access after sleep

Please download and run EtreCheck (the free version, don’t need the paid version here), and use the Share to share the results to the Mac clipboard. Then open a new reply here, and press the Additional Text button (the button that looks like a printed page), and paste and post the hardware and software configuration report here. From that, we can get a little more detail about what is installed and what is running here.

Are you connecting to the Gateway/Router with both Ethernet and Wi-Fi...?

I'm asking because your Network section shows both Ethernet and Wi-Fi services.

Plus it shows the Ethernet service at the top of the service order list.

If you are not using the Ethernet service...?

Remove it from the Network list and/or move the Wi-Fi service to the top of the service order list.

see > Change the order of the network services your Mac uses - Apple Support

Then if setting Wi-Fi at the top of the service order doesn't help...?

see > If your Mac isn't connecting to the internet over Wi-Fi - Apple Support

See if turning off screen sharing makes a difference.

Turn Mac screen sharing on or off - Apple Support

I don’t see any of the usual suspect apps, but do see a loaded system, and with crashes.

I would remove the HP app, and would take a look at the local network.

Which (presumably) HP printer model is in use here?

Nobodyknowsimadog wrote:

I don't know how to interpret "loaded" and "take a look at."

Loaded: Full, using the available capacity of the hardware. Systems that are loaded tend to have performance issues.

To take a look at: to see if the printer is accessible, as well as the router, but the Wi-Fi “join” setting mentioned later is certainly involved here.

I use an HP Envy 6110e which I rent from HP. If I delete their app, I don't know how I will control the printer, check my page usage, etc.

One might wonder whether HP might charge each time their app crashes, too?