```
Ping messages are an application-level mechanism. Move timeout
logic from net to net processing.
```
Partial backport of [[https://github.com/bitcoin/bitcoin/pull/20721 | core#20721]]:
https://github.com/bitcoin/bitcoin/pull/20721/commits/dd2646d12c172cb8899669af717c590483a17404
Ref T1696.
Depends on D10876.