Can Nikon D5600 wifi connect directly to a PC or Mac computer?

Well, if you really need to, you could tether over wifi, e.g. https://www.tethertools.com/product/case-air-wireless-tethering-system/

A cheaper solution would be USB tethering (see https://www.tethertools.com/camera/nikon-d5600/ ) But bear in mind that cables not only limit your movement, but can also be a big risk. A yanked cable can topple a camera and ports are often soldered directly to the logic boards of the cameras, so a hard yank could mean logic board replacement (costly and probably not covered by warranty).

You might also be able to use an Android or iOS emulator on a Mac or PC to run SnapBridge, but since that gets into file-system access, you may run into limitations of the emulator. Such emulators are commonly used when developing/testing mobile apps.

As far as I know Nikon thought that these "smart" features with the wireless control of the camera and direct storing of the images on the device is only needed on smart devices like phones and tablets and therefore they just released apps for these platforms. In older versions, where only wifi was needed this could be solved by other platforms but in your camera series (like other of that time) Nikon build it with Bluetooth and the app sends a special signal to the camera every couple of minutes. If the camera does not receive this signal the wifi is deactivated and here is the main problem that there is no solution for this, at least none which is known to me. For our luck Nikon corrected this with their new cameras.

The cheapest possibility to solve this problem that I know is to do it with an extra wireless router running DslrDashboardServer and the computer running qDslrDashboard.

With this method you reconfigure the router to run the software and directly connect to the computer. On the computer you qDslrDashboard to directly download it in a folder and for example LightRoom to monitor this Folder and autoimporting the images. You can also control the camera via qDslrDashboard.

The disadvantage of this method is that you have a small router connected via a cable to the camera which you have to carry around.

This needs some diy stuff but can work quite well.

Another possibility to solve this problem is to buy a commercial third party connector and do the connection via this and the software connected to it, like from Tethertools

btw: If you tether it by cable you can also use just qDslrDashboard for this and have no need to do the router stuff.

As far as I am aware, the above description of Bluetooth controlling the WiFi link is correct - certainly that's what seems to be happening using Snapbridge. What I've tried doing is connecting to the D5600 via Bluetooth using Snapbridge on my tablet, and choosing Remote photography. Snapbridge then fires up the cameras WiFi hotspot and connects to it. At this point you may be able to connect a PC to the camera via WiFi.

However, you need to know the SSID and its passcode. The former will most likely be displayed by your PC, so the real problem is the latter, however you can change it in the camera's configuration menu, before launching the remote connection as in the above paragraph. At this point, given the SSID and the passcode, you should be able to connect, however, for me at least, and I suspect many others, there remains another problem.

That is that you can't seem to alter the hotspot's IP Range, which is hardcoded to 192.168.1.*. As that is the same range coming from my router, to which my laptop is connected via cable, the PC throws a wobbly, won't connect to the WiFi hotspot, but nevertheless temporarily kills the cabled connection while it tries. I could test this further by reassigning the ranges given out by my router, but frankly, ICBA. I simply connect to the camera via USB, which does come up in explorer just like a mobile phone or tablet.

My HP PC has an HDMI input, and yes you can connect with out purchasing any HDMI to USB capture device. Check if your PC has a HDMI in port. Plug in directly.