Feature Request for AdGuardHome

### 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

- [x] 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

Due to the potential DNS pollution in China, many global DNS servers, whether DoH or DoT, may fail to connect. When testing upstream DNS servers in AdGuardHome, errors like "tls://familyshield.sse.cisco.com:853"：Unable to use, please check whether your input is correct may occur. These error messages pop up separately, making it inconvenient for users to screen out the available DNS servers.

### Proposed solution

*It would be great if AdGuardHome could automatically test or ping upstream DNS servers in idle time to determine which ones are available and output the results to the log. If this is not feasible, it would be helpful to merge the error messages about unavailable upstream DNS servers into one pop-up window, so that users can better screen out the available ones.

### Alternatives considered and additional information

_No response_