addon-cloudflared: Problem with connection with Cloudflared 4.0.8 (and latest HA version)

The problem

I get a lot of these after updating Cloudflared and HA to latest version. Never had ANY connection issues before – it just worked like it was not there. I get these problems both in browser and in iPhone app. It is worst with the things that take some time to load, like Node Red dashboard - that I can hardly access anymore because it just stops loading when non on local wifi.

What version of Cloudflared has the issue?

4.0.8

What was the last working version of Cloudflared?

4.0.7

What type of installation are you running?

Home Assistant OS

Add-on YAML Configuration

No response

Anything in the logs that might be useful for us?

A lot of these:

2023-01-19T15:26:53Z ERR Request failed error="Unable to reach the origin service. The service may be down or it may not be responding to traffic from cloudflared: dial tcp 172.30.32.1:8123: connect: connection refused" connIndex=0 dest=https://xxx.xxx.xxx/api/websocket ip=xxx.xxx.xxx.xxx type=ws
2023-01-19T17:06:28Z ERR  error="Unable to reach the origin service. The service may be down or it may not be responding to traffic from cloudflared: dial tcp: lookup homeassistant on 127.0.0.11:53: read udp 127.0.0.1:35133->127.0.0.11:53: i/o timeout" cfRay=78c128a64c030b55-OSL ingressRule=0 originService=http://homeassistant:8123

Steps to reproduce the issue

Cannot really say

Additional information

Running on RPi3, everything else is normal, but Cloudflared is acting up.