If anyone stumbles across the same phenomenon, here's what I found out (spoiler: I'm stupid):
Of course, what should have immediately raised an alarm was the fact that I wrote openwsmand when the xapi process is actually responsible for handling connection attempts from XenCenter and the likes. What happened here was that I just did a simple netstat -plant and noticed that openwsmand was listening at port 443, which I knew was the port that XenCenter tried to connect to, so I assumed this was the right process.
But of course, XenCenter can't connect to openwsmand because this is a tool of the OpenManage Suite by Dell. I suppose that when I first installed OpenManage, openwsmand tried to bind to port 443, but this was already in use by xapi, so it gave up and I was still able to connect.
When I restarted the machine, however, the openwsmand service was started before xapi, so it occupied port 443, leaving me with no possibility to connect using XenCenter.
A simple
$ service openwsmand stop
$ xe-toolstack-restart
$ service openwsmand start
fixed the problem. Currently running VMs won't be affected by this operation.
Best Answer
Never mind. It was a silly error of non-matching IP addresses. I had set up XenServer to use DHCP for IP addresses and it configured it using the BMC IP address, not the ethernet port IP address. I basically fixed this error by going on XenServer and selecting "Network and Management Interface" and then changing IP address statically to the right number.