[PROF-11306] Upgrade libdatadog dependency to 16.0.1

**What does this PR do?**

This PR upgrades the datadog gem to use libdatadog 16.0.1.

It includes a few changes to match breaking API updates in
crashtracking.

**Motivation:**

Libdatadog 16 is needed to unblock
#4331 .

This version also brings a few crashtracking improvements.

**Change log entry**

Yes. Upgrade libdatadog dependency to 16.0.1

**Additional Notes:**

As usual, I'm opening this PR as a draft as libdatadog 16.0.1 is not
yet available on rubygems.org, and I'll come back to re-trigger CI
and mark this as non-draft once it is.

**How to test the change?**

Our existing test coverage includes libdatadog testing, so a green C
is good here :)

datadog.gemspec

@@ -69,7 +69,7 @@ Gem::Specification.new do |spec|
 
   # When updating the version here, please also update the version in `libdatadog_extconf_helpers.rb`
   # (and yes we have a test for it)
-  spec.add_dependency 'libdatadog', '~> 14.3.1.1.0'
+  spec.add_dependency 'libdatadog', '~> 16.0.1.1.0'
 
   # Will no longer be a default gem on Ruby 3.5, see
   # https://github.com/ruby/ruby/commit/d7e558e3c48c213d0e8bedca4fb547db55613f7c and

ext/libdatadog_extconf_helpers.rb

@@ -8,7 +8,7 @@ module Datadog
   module LibdatadogExtconfHelpers
     # Used to make sure the correct gem version gets loaded, as extconf.rb does not get run with "bundle exec" and thus
     # may see multiple libdatadog versions. See https://github.com/DataDog/dd-trace-rb/pull/2531 for the horror story.
-    LIBDATADOG_VERSION = '~> 14.3.1.1.0'
+    LIBDATADOG_VERSION = '~> 16.0.1.1.0'
 
     # Used as an workaround for a limitation with how dynamic linking works in environments where the datadog gem and
     # libdatadog are moved after the extension gets compiled.