Thanks for your time and your answer!
While checking the forum I just noticed that somebody else has a similar problem which also occurs with stubby.
Following that thread I delayed the stubby startup by 30 seconds so it starts after pihole-FTL now.
However, that's only a workaround, as it doesn't solve the problem.
If everything is running (pihole-FTL first, stubby afterwards) this is the result of the command:
tcp 0 0 127.0.0.1:4711 0.0.0.0:* LISTEN 2455/pihole-FTL
tcp 0 0 0.0.0.0:80 0.0.0.0:* LISTEN 738/nginx: master p
tcp 0 0 0.0.0.0:53 0.0.0.0:* LISTEN 2455/pihole-FTL
tcp6 0 0 ::1:4711 :::* LISTEN 2455/pihole-FTL
tcp6 0 0 :::80 :::* LISTEN 738/nginx: master p
tcp6 0 0 :::53 :::* LISTEN 2455/pihole-FTL
udp 0 0 0.0.0.0:53 0.0.0.0:* 2455/pihole-FTL
udp 0 0 127.0.0.2:53 0.0.0.0:* 1397/stubby
udp6 0 0 :::53 :::* 2455/pihole-FTL
If only stubby is running:
tcp 0 0 0.0.0.0:80 0.0.0.0:* LISTEN 738/nginx: master p
tcp 0 0 127.0.0.2:53 0.0.0.0:* LISTEN 23020/stubby
tcp6 0 0 :::80 :::* LISTEN 738/nginx: master p
udp 0 0 127.0.0.2:53 0.0.0.0:* 23020/stubby
If only pihole-FTL is running:
tcp 0 0 127.0.0.1:4711 0.0.0.0:* LISTEN 23252/pihole-FTL
tcp 0 0 0.0.0.0:80 0.0.0.0:* LISTEN 738/nginx: master p
tcp 0 0 0.0.0.0:53 0.0.0.0:* LISTEN 23252/pihole-FTL
tcp6 0 0 ::1:4711 :::* LISTEN 23252/pihole-FTL
tcp6 0 0 :::80 :::* LISTEN 738/nginx: master p
tcp6 0 0 :::53 :::* LISTEN 23252/pihole-FTL
udp 29248 0 0.0.0.0:53 0.0.0.0:* 23252/pihole-FTL
udp6 0 0 :::53 :::* 23252/pihole-FTL