Add WLAN to old pc

Those are PCI and not PCI-e slots it's very unlikely to find PCI WiFi cards. You can use a USB WiFi adapter.

As has been said, an older PCI card may not be what you want as it may not be compatible with the (I assume) WPA3 encryption your router is configured with. Instead, just get a USB adapter like the one linked above.

Also at least in the short term you could probably use usb tethering to basically turn a mobile into a usb wifi adapter.

And I realised your link for the motherboard doesn't match the photo. The link shows a board with a pci-e x1 slot and 1 pci slot while the photo has 2 pci slots.

As Spear said a cheap mini pc is worth serious consideration at this point, especially if they are running Windows, or check what's available from a local cex. Just make sure anything you are considering will connect to whatever monitor they are using unless you want to upgrade that at the same time (which might make more sense then buying an adapter given the likely age of stuff we are looking at) ;)

I think the power savings are overstated. But I'd also replace it with a cheap small box that would run modern software better. Something used off adverts.

Two video cassettes you say! Are we talking VHS or betamax? My sources tell me betamax is the future ;-)

Dual core? That's a bit old.

It's a bit lite even for a media server. It's the OP looking for a media server?

I agree though the OP should just get some small form factor PC used off adverts. Just not a dual core.

Fair enough