…8106)

## Summary of changes

Implements [Andrea's
specification](https://docs.google.com/document/d/1c47iSTWxIOHMHfZTF2nT9xfyQaIBP9KJvI9sRn5SvpM/edit?tab=t.0#heading=h.uoivahvmuvbg).
TLDR: We need to send in process tags whether the service used is the
one set by the user or the default one.
It was deemed acceptable not to handle the case where the service is set
at the scope level when creating spans, so we focus on service set by
the user through config.

## Reason for change
Service renaming shouldn't rename a service if it's the one set by the
customer but the backend doesn't know that today

## Implementation details
- As the service can be changed in the settings, I moved the process
tags in the `MutableSettings`. As a side effect it simplifies part of
the code as we don't have to pass service tags anymore as they're in
Settings.
- The ProcessTags object is null when the PropagateServiceTag config key
is false. We rely in the rest of the code on whether the tags are null
or not.
- Process tags are still lazily initialized. The `ProcessTags` class is
merely a container of the information needed when you need to serialize
them.

## Test coverage
Utests mainly.
There are system tests to update once merged:
DataDog/system-tests#6204

## Other details
AI generated and polished by hand (and repolished again :p) 

APMLP-1000

---------

Signed-off-by: Pierre Bonet <pierre.bonet@datadoghq.com>
Co-authored-by: Andrew Lock <andrew.lock@datadoghq.com>
Co-authored-by: Raphaël Vandon <raphael.vandon@datadoghq.com>
Co-authored-by: Raphaël Vandon <raphael.vandon@datadog.com>