chore(propagation): add context span links to span correctly (#7658)

Not a fix because this feature hasn't been released yet. The logic
before was incorrect, because we never would have context span links at
that point. This also adds a test using fastapi to assure our root span
actually has the links added correctly, while child spans do not.

## Checklist

- [x] Change(s) are motivated and described in the PR description.
- [x] Testing strategy is described if automated tests are not included
in the PR.
- [x] Risk is outlined (performance impact, potential for breakage,
maintainability, etc).
- [x] Change is maintainable (easy to change, telemetry, documentation).
- [x] [Library release note
guidelines](https://ddtrace.readthedocs.io/en/stable/releasenotes.html)
are followed. If no release note is required, add label
`changelog/no-changelog`.
- [x] Documentation is included (in-code, generated user docs, [public
corp docs](https://github.com/DataDog/documentation/)).
- [x] Backport labels are set (if
[applicable](https://ddtrace.readthedocs.io/en/latest/contributing.html#backporting))

## Reviewer Checklist

- [ ] Title is accurate.
- [ ] No unnecessary changes are introduced.
- [ ] Description motivates each change.
- [ ] Avoids breaking
[API](https://ddtrace.readthedocs.io/en/stable/versioning.html#interfaces)
changes unless absolutely necessary.
- [ ] Testing strategy adequately addresses listed risk(s).
- [ ] Change is maintainable (easy to change, telemetry, documentation).
- [ ] Release note makes sense to a user of the library.
- [ ] Reviewer has explicitly acknowledged and discussed the performance
implications of this PR as reported in the benchmarks PR comment.
- [ ] Backport labels are set in a manner that is consistent with the
[release branch maintenance
policy](https://ddtrace.readthedocs.io/en/latest/contributing.html#backporting)
- [ ] If this PR touches code that signs or publishes builds or
packages, or handles credentials of any kind, I've requested a review
from `@DataDog/security-design-and-guidance`.
- [ ] This PR doesn't touch any of that.

Author: ZStriker19

.riot/requirements/19de4fb.txt

@@ -0,0 +1,35 @@
+#
+# This file is autogenerated by pip-compile with Python 3.12
+# by the following command:
+#
+#    pip-compile --no-annotate .riot/requirements/19de4fb.in
+#
+annotated-types==0.6.0
+anyio==3.7.1
+attrs==23.1.0
+certifi==2023.7.22
+coverage[toml]==7.3.2
+fastapi==0.104.1
+h11==0.14.0
+httpcore==1.0.2
+httpretty==1.1.4
+httpx==0.25.1
+hypothesis==6.45.0
+idna==3.4
+iniconfig==2.0.0
+mock==5.1.0
+msgpack==1.0.7
+opentracing==2.4.0
+packaging==23.2
+pluggy==1.3.0
+pydantic==2.5.1
+pydantic-core==2.14.3
+pytest==7.4.3
+pytest-cov==4.1.0
+pytest-mock==3.12.0
+sniffio==1.3.0
+sortedcontainers==2.4.0
+starlette==0.27.0
+structlog==23.2.0
+typing-extensions==4.8.0
+wheel==0.41.3

.riot/requirements/1bd153a.txt

@@ -2,26 +2,38 @@
 # This file is autogenerated by pip-compile with Python 3.7
 # by the following command:
 #
-#    pip-compile --config=pyproject.toml --no-annotate --resolver=backtracking .riot/requirements/1a8dea8.in
+#    pip-compile --config=pyproject.toml --no-annotate --resolver=backtracking .riot/requirements/1c3e1e3.in
 #
+annotated-types==0.5.0
+anyio==3.7.1
 attrs==23.1.0
+certifi==2023.7.22
 coverage[toml]==7.2.7
 exceptiongroup==1.1.3
+fastapi==0.103.2
+h11==0.14.0
+httpcore==0.17.3
 httpretty==1.1.4
+httpx==0.24.1
 hypothesis==6.45.0
+idna==3.4
 importlib-metadata==6.7.0
 iniconfig==2.0.0
 mock==5.1.0
 msgpack==1.0.5
 opentracing==2.4.0
-packaging==23.1
+packaging==23.2
 pluggy==1.2.0
-pytest==7.4.0
+pydantic==2.5.1
+pydantic-core==2.14.3
+pytest==7.4.3
 pytest-cov==4.1.0
 pytest-mock==3.11.1
+sniffio==1.3.0
 sortedcontainers==2.4.0
+starlette==0.27.0
 structlog==23.1.0
 tomli==2.0.1
 typing-extensions==4.7.1
-wheel==0.41.2
+wheel==0.41.3
 zipp==3.15.0

.riot/requirements/1a8dea8.txt renamed to .riot/requirements/1c3e1e3.txt

@@ -0,0 +1,35 @@
+#
+# This file is autogenerated by pip-compile with Python 3.12
+# by the following command:
+#
+#    pip-compile --no-annotate .riot/requirements/1cade2e.in
+#
+annotated-types==0.6.0
+anyio==3.7.1
+attrs==23.1.0
+certifi==2023.7.22
+coverage[toml]==7.3.2
+fastapi==0.104.1
+h11==0.14.0
+httpcore==1.0.2
+httpretty==1.1.4
+httpx==0.25.1
+hypothesis==6.45.0
+idna==3.4
+iniconfig==2.0.0
+mock==5.1.0
+msgpack==1.0.7
+opentracing==2.4.0
+packaging==23.2
+pluggy==1.3.0
+pydantic==2.5.1
+pydantic-core==2.14.3
+pytest==7.4.3
+pytest-cov==4.1.0
+pytest-mock==3.12.0
+sniffio==1.3.0
+sortedcontainers==2.4.0
+starlette==0.27.0
+structlog==23.2.0
+typing-extensions==4.8.0
+wheel==0.41.3

.riot/requirements/1c83510.txt

@@ -0,0 +1,37 @@
+#
+# This file is autogenerated by pip-compile with Python 3.9
+# by the following command:
+#
+#    pip-compile --no-annotate .riot/requirements/1d15302.in
+#
+annotated-types==0.6.0
+anyio==3.7.1
+attrs==23.1.0
+certifi==2023.7.22
+coverage[toml]==7.3.2
+exceptiongroup==1.1.3
+fastapi==0.104.1
+h11==0.14.0
+httpcore==1.0.2
+httpretty==1.1.4
+httpx==0.25.1
+hypothesis==6.45.0
+idna==3.4
+iniconfig==2.0.0
+mock==5.1.0
+msgpack==1.0.7
+opentracing==2.4.0
+packaging==23.2
+pluggy==1.3.0
+pydantic==2.5.1
+pydantic-core==2.14.3
+pytest==7.4.3
+pytest-cov==4.1.0
+pytest-mock==3.12.0
+sniffio==1.3.0
+sortedcontainers==2.4.0
+starlette==0.27.0
+structlog==23.2.0
+tomli==2.0.1
+typing-extensions==4.8.0
+wheel==0.41.3

.riot/requirements/1cade2e.txt

@@ -0,0 +1,37 @@
+#
+# This file is autogenerated by pip-compile with Python 3.10
+# by the following command:
+#
+#    pip-compile --no-annotate .riot/requirements/6e1a0eb.in
+#
+annotated-types==0.6.0
+anyio==3.7.1
+attrs==23.1.0
+certifi==2023.7.22
+coverage[toml]==7.3.2
+exceptiongroup==1.1.3
+fastapi==0.104.1
+h11==0.14.0
+httpcore==1.0.2
+httpretty==1.1.4
+httpx==0.25.1
+hypothesis==6.45.0
+idna==3.4
+iniconfig==2.0.0
+mock==5.1.0
+msgpack==1.0.7
+opentracing==2.4.0
+packaging==23.2
+pluggy==1.3.0
+pydantic==2.5.1
+pydantic-core==2.14.3
+pytest==7.4.3
+pytest-cov==4.1.0
+pytest-mock==3.12.0
+sniffio==1.3.0
+sortedcontainers==2.4.0
+starlette==0.27.0
+structlog==23.2.0
+tomli==2.0.1
+typing-extensions==4.8.0
+wheel==0.41.3