chore: fixes for clippy changes in Rust 1.74 (tokio-rs#2814)

With the release of Rust 1.74, there are some new or modified clippy
lints that need adaption in the code.

The main change was the removal of the `private_in_public`.
https://rust-lang.github.io/rfcs/2145-type-privacy.html

Then two more changes were required, in one case to adhere a lint and
the other to allow it. When talking about what an "application" needs to
do when setting up `tracing-error`, it makes sense to include `fn
main()` in the doctest, even though the lint recommends against it.
; Conflicts:
;	examples/examples/map-traced-error.rs

tracing-appender/src/lib.rs

@@ -153,7 +153,8 @@
  overflowing_literals,
  path_statements,
  patterns_in_fns_without_body,
- private_in_public,
+ private_interfaces,
+ private_bounds,
  unconditional_recursion,
  unused,
  unused_allocation,

tracing-attributes/src/lib.rs

@@ -70,7 +70,8 @@
  overflowing_literals,
  path_statements,
  patterns_in_fns_without_body,
- private_in_public,
+ private_interfaces,
+ private_bounds,
  unconditional_recursion,
  unused_allocation,
  unused_comparisons,

tracing-core/src/lib.rs

@@ -135,7 +135,8 @@
  overflowing_literals,
  path_statements,
  patterns_in_fns_without_body,
- private_in_public,
+ private_interfaces,
+ private_bounds,
  unconditional_recursion,
  unused,
  unused_allocation,

tracing-error/src/lib.rs

@@ -183,6 +183,7 @@
  html_logo_url = "https://raw.githubusercontent.com/tokio-rs/tracing/master/assets/logo-type.png",
  issue_tracker_base_url = "https:/tokio-rs/tracing/issues/"
 )]
+#![allow(clippy::needless_doctest_main)]
 #![warn(
  missing_debug_implementations,
  missing_docs,
@@ -196,7 +197,8 @@
  overflowing_literals,
  path_statements,
  patterns_in_fns_without_body,
- private_in_public,
+ private_interfaces,
+ private_bounds,
  unconditional_recursion,
  unused,
  unused_allocation,

tracing-flame/src/lib.rs

@@ -124,7 +124,8 @@
  overflowing_literals,
  path_statements,
  patterns_in_fns_without_body,
- private_in_public,
+ private_interfaces,
+ private_bounds,
  unconditional_recursion,
  unused,
  unused_allocation,

tracing-futures/src/lib.rs

@@ -87,7 +87,8 @@
  overflowing_literals,
  path_statements,
  patterns_in_fns_without_body,
- private_in_public,
+ private_interfaces,
+ private_bounds,
  unconditional_recursion,
  unused,
  unused_allocation,

tracing-log/src/lib.rs

@@ -112,7 +112,8 @@
  overflowing_literals,
  path_statements,
  patterns_in_fns_without_body,
- private_in_public,
+ private_interfaces,
+ private_bounds,
  unconditional_recursion,
  unused,
  unused_allocation,

tracing-serde/src/lib.rs

@@ -174,7 +174,8 @@
  overflowing_literals,
  path_statements,
  patterns_in_fns_without_body,
- private_in_public,
+ private_interfaces,
+ private_bounds,
  unconditional_recursion,
  unused,
  unused_allocation,

tracing-subscriber/src/lib.rs

@@ -186,7 +186,8 @@
  overflowing_literals,
  path_statements,
  patterns_in_fns_without_body,
- private_in_public,
+ private_interfaces,
+ private_bounds,
  unconditional_recursion,
  unused,
  unused_allocation,

tracing-tower/src/lib.rs

@@ -16,7 +16,8 @@
  overflowing_literals,
  path_statements,
  patterns_in_fns_without_body,
- private_in_public,
+ private_interfaces,
+ private_bounds,
  unconditional_recursion,
  unused,
  unused_allocation,

tracing/src/lib.rs

@@ -929,7 +929,8 @@
  overflowing_literals,
  path_statements,
  patterns_in_fns_without_body,
- private_in_public,
+ private_interfaces,
+ private_bounds,
  unconditional_recursion,
  unused,
  unused_allocation,