My server becomes slow when resolving DNS while experiencing issues to https://family.adguard-dns.com:443/dns-query

### Prerequisites

- [X] I have checked the [Wiki](https://github.com/AdguardTeam/AdGuardHome/wiki) and [Discussions](https://github.com/AdguardTeam/AdGuardHome/discussions) and found no answer

- [ ] I have searched other issues and found no duplicates

- [X] I want to request a feature or enhancement and not ask a question

### The problem

There are many errors in my AdGuard Home logs with the following error like this:

```
2024/09/19 16:04:40.210170 [error] dnsproxy: https://family.adguard-dns.com:443/dns-query: response received over tcp: "reading https://family.adguard-dns.com:443/dns-query: net/http: request canceled (Client.Timeout or context cancellation while reading body)"
2024/09/19 16:04:41.953981 [error] dnsproxy: https://family.adguard-dns.com:443/dns-query: response received over tcp: "reading https://family.adguard-dns.com:443/dns-query: net/http: request canceled (Client.Timeout or context cancellation while reading body)"
2024/09/19 16:04:42.170730 [error] dnsproxy: https://family.adguard-dns.com:443/dns-query: response received over tcp: "requesting https://family.adguard-dns.com:443/dns-query: Get \"https://family.adguard-dns.com:443/dns-query?dns=AAABAAABAAAAAAAABDk4MTUCcGMDZG5zB2FkZ3VhcmQDY29tAAAQAAE\": net/http: request canceled (Client.Timeout exceeded while awaiting headers)"
2024/09/19 16:04:42.870441 [error] dnsproxy: https://family.adguard-dns.com:443/dns-query: response received over tcp: "requesting https://family.adguard-dns.com:443/dns-query: Get \"https://family.adguard-dns.com:443/dns-query?dns=AAABAAABAAAAAAAABDA2ODcCcGMDZG5zB2FkZ3VhcmQDY29tAAAQAAE\": net/http: request canceled (Client.Timeout exceeded while awaiting headers)"
2024/09/19 16:04:44.874861 [error] dnsproxy: https://family.adguard-dns.com:443/dns-query: response received over tcp: "reading https://family.adguard-dns.com:443/dns-query: net/http: request canceled (Client.Timeout or context cancellation while reading body)"
```

When this error appears, I tried to test the ping, and it turns out my server is having connection issues with family.adguard-dns.com. Here is the ping test with 100 packets to family.adguard-dns.com.


I'm not sure whether this is due to my poor connection or an issue with the DNS server, but this error is really making AdGuard Home very slow when resolving DNS. When I ping all the upstream servers I use, I don't experience any connection issues like I do with family.adguard-dns.com.

### Proposed solution

There is another issue like https://github.com/AdguardTeam/AdGuardHome/issues/7175 and https://github.com/AdguardTeam/AdGuardHome/issues/6817 the solution was to disable 'Use AdGuard browsing security web service' and 'Use AdGuard parental control web service'. But I think there should be a better solution.

Perhaps instead of 'forcing' the connection to family.adguard-dns.com when enabling the 'Use AdGuard browsing security web service' and 'Use AdGuard parental control web service' while the server is down from the client side, we could switch to another server with the same functionality as family.adguard-dns.com. If my connection is truly experiencing issues, I might understand why my DNS is slow to resolve.

### Alternatives considered and additional information

_No response_