Merge #4410

4410: Implement the experimental log mode cli flag and log level updates at runtime r=dureuill a=irevoire

# Pull Request
This PR fixes two issues at once because they’re highly correlated in the codebase.

## Related issue
Fixes https://github.com/meilisearch/meilisearch/issues/4415
Fixes https://github.com/meilisearch/meilisearch/issues/4413

## What does this PR do?
- It makes the fmt logger configurable to output json or human-readable logs (like we already do today)
- It moves the fmt logger under a `reload` layer so we can update its targets at runtime
- Add the possibility to stream logs in the json mode
- Adds an analytics for the new CLI flag

Co-authored-by: Tamo <tamo@meilisearch.com>

Cargo.lock

@@ -5197,6 +5197,16 @@ dependencies = [
  "tracing-core",
 ]
 
+[[package]]
+name = "tracing-serde"
+version = "0.1.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "bc6b213177105856957181934e4920de57730fc69bf42c37ee5bb664d406d9e1"
+dependencies = [
+ "serde",
+ "tracing-core",
+]
+
 [[package]]
 name = "tracing-subscriber"
 version = "0.3.18"
@@ -5204,11 +5214,14 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "ad0f048c97dbd9faa9b7df56362b8ebcaa52adb06b498c050d2f4e32f90a7a8b"
 dependencies = [
  "nu-ansi-term",
+ "serde",
+ "serde_json",
  "sharded-slab",
  "smallvec",
  "thread_local",
  "tracing-core",
  "tracing-log",
+ "tracing-serde",
 ]
 
 [[package]]