Add --debug option

[strzibny]

Let's add --debug option for better debugging logs when customers face something unexpected regarding connections and timeouts.

Debug mode adds tracing for each request to stderr with wall-clock and elapsed timestamps; DNS, TCP connect (local -> remote address), TLS handshake, time to first byte, response status and headers, and body size.

For searches, we also correlate the server's search_metadata timestamps with the client timeline and flag whether a long wait happened before the search was created, during processing, or after processing finished.

[ilyazub]

Opus 5.5 Max wrote this:
#17 is merged (7acfb80); against main this PR now conflicts in 3 files (README.md, pkg/api/client.go, pkg/cmd/root.go). On main, errors and warnings go to stderr as one JSON line each, and in a 120-command matrix every stderr line of a non-interactive run was JSON; scripts and agents parse stderr line by line, so plain [debug] lines would break that. Printing them as JSON lines, such as {"debug":{...}}, when stderr isn't a terminal, and as plain text on one, keeps it; login and the no-command usage already split this way.