I followed the wiki article and have unbound now running and working (using port 15353 sice 5353 is in use).
sudo pihole -a localdnsport 15353
Does not work for me, it seems to not support the localdnsport option. Configuring from the web console is also not possible since it does not list the "local DNS server on custom port" options as seen in the screenshots.
pihole up shows the system as up to date. What am I doing wrong here?
What's the output of pihole -v?
pi@piholea:~ $ pihole -v
Pi-hole version is v3.3.1 (Latest: v3.3.1)
AdminLTE version is v3.3 (Latest: v3.3)
FTL version is v3.0 (Latest: v3.0)
Running on latest raspberry pi.
As I said
Okay, I missed that 
I suppose this is still under development.
Let me know if I can help test.
You can join us in the current beta testing phase of Pi-hole v4.0 if you like. Here, this is already available. See this for further details:
I switched to the FTLDNS branch and everything works. 
My one remaining question:
port 5353 is by default in use by avahi-daemon according to netstat -anp. I have therefore configured unbound on 15353. I followed the wiki exactly. Wont there be a conflict with avahi if both try to open port 5353?
You can change the port in the unbound config, to some other port that will not conflict.
First you need to stop unbound, change the config, restart unbound and update the port in Pi-hole.