All apps on Apple TV 4K are not working

It is clearly online on my WiFi network.

How so? What checks did you do, or what confirmation do you have?

From your description so far, it isn’t clear at all.

Does your Apple TV box have the expected local IP address, within the range that your router should lease for? Often 192.168.x.x (10.x.x.x and 172.x.x.x are also valid, but are not much used on home networks, due to their much bigger range (i.e. a million devices or more)) [1]. But it should not be 169.254.x.x, which would be self-assigned and non-communicating for the internet [2].

See Settings﹥Network﹥… for this data.

Let us know if that applies to your situation.

… doing a reset, which I really would like to avoid.

When choosing that, see here for instructions: Reset or restore your Apple TV to its factory settings - Apple Support

If so, will all of my apps and data automatically be restored once I log in to my Apple account?

No. After a reset, the device will have to be reconfigured “as new”.

Or must I manually download all apps and manually log in to each app.

The App Store app will list previously downloaded apps for the account, filtered for compatibility with the current device, so that makes it a tiny bit easier.

Apps that have their own content provider account, will each have to be signed in one at a time.

Third party apps that rely on your TV provider plan may get automatic sign-in, when you enter those credentials once for all such apps.

Third party apps that have a plan through your Apple Account may require to do “Restore Purchases” from within each app.

Apple’s own apps would take their sign-in from the active user account.

Performing a reset on your Apple TV will likely resolve the issues with the apps not working. After the reset, you will need to log in to your Apple account again, and your apps should re-download automatically.

IP and router address seem about right, and in the same range, so that looks to be okay.

Next, if you can, please access the router settings. This is often accessible by going to the router address in a web browser on a computer. It would have a separate sign-in, so that only the owner can make changes. I would expect the router settings to be able to show a list of connected devices, and their status.

Mine shows a green globe next to devices that are internet connected. Your router settings may look a bit different, depending on brand, model, and software (version).

Another thing is that your chosen DNS server might be down, overwhelmed, or otherwise unavailable temporarily. Try an alternative. You may set the Apple TV DNS to ‘Automatic’, then Apple TV will use the DNS server list settings as defined on the router. Or you may enter a single manual DNS directly on Apple TV. Automatic has the benefit of multiple DNSes, so that a secondary can be tried if the primary is unavailable. For most users, the DNS servers from their ISP are not only fine, but also the fastest.