So I just “successfully” restored the influxdb add-on on my new host. Problem is that the add-on itself is running, I can see it in htop:
and the log tab of the add-on is also populated every minute:
[httpd] 127.0.0.1 - kapacitor [15/Aug/2022:12:32:03 +0100] "GET /ping HTTP/1.1" 204 0 "-" "KapacitorInfluxDBClient" e2bf908b-1c8d-11ed-8437-0242ac1e2107 102
[httpd] 127.0.0.1 - kapacitor [15/Aug/2022:12:32:03 +0100] "POST /query?db=&q=SHOW+DATABASES HTTP/1.1 " 200 116 "-" "KapacitorInfluxDBClient" e2bfede9-1c8d-11ed-8438-0242ac1e2107 1197
[httpd] 127.0.0.1 - kapacitor [15/Aug/2022:12:32:03 +0100] "POST /query?db=&q=SHOW+RETENTION+POLICIES+ON+_internal HTTP/1.1 " 200 153 "-" "KapacitorInfluxDBClient" e2c06c6f-1c8d-11ed-8439-0242ac1e2107 3427
[httpd] 127.0.0.1 - kapacitor [15/Aug/2022:12:32:03 +0100] "POST /query?db=&q=SHOW+RETENTION+POLICIES+ON+hass HTTP/1.1 " 200 149 "-" "KapacitorInfluxDBClient" e2c148a7-1c8d-11ed-843a-0242ac1e2107 1809
[httpd] 127.0.0.1 - kapacitor [15/Aug/2022:12:32:03 +0100] "POST /query?db=&q=SHOW+SUBSCRIPTIONS HTTP/1.1 " 200 220 "-" "KapacitorInfluxDBClient" e2c1ca91-1c8d-11ed-843b-0242ac1e2107 1301
[httpd] 172.30.33.5 - hass [15/Aug/2022:12:32:08 +0100] "GET /query?db=hass&epoch=s&q=SELECT+mean%28%22value%22%29+FROM+%22+%22+WHERE+%22entity_id%22+%3D+%27load_1m%27+AND+time+%3E+1660562828579ms+and+time+%3C+1660563128579ms+GROUP+BY+time%281s%29+fill%28none%29+ORDER+BY+time+ASC%3B HTTP/1.1" 200 57 "-" "Grafana" e5a02ae6-1c8d-11ed-843c-0242ac1e2107 1847
the info tab of the add-on states it’s not running and doesn’t offer me to restart the add-on:
Accessing the web-ui is also not possible. 
I tried already a ha-restart but it looks like (even start on boot is disabled) the add-on starts on his own (or just continues to run?)
The exact same also happens for the grafana add-on I just restored. For this one I even did run a update of the add-on (so a restart of the add-on happened) but still it’s just a “ghost runner”. 
Any hints what to try to get the add-ons working again?