docs: add some words about specifying conflicting extras/groups (#9120)

This doesn't cover the optional `package` key since I wasn't quite sure
how to articulate its utility in a digestible way.

---------

Co-authored-by: Zanie Blue <contact@zanie.dev>

docs/concepts/dependencies.md

@@ -389,6 +389,11 @@ To add an optional dependency, use the `--optional <extra>` option:
 $ uv add httpx --optional network
 ```
 
+!!! note
+
+    If you have optional dependencies that conflict with one another, resolution will fail
+    unless you explicitly [declare them as conflicting](./projects.md#optional-dependencies).
+
 ## Development dependencies
 
 Unlike optional dependencies, development dependencies are local-only and will _not_ be included in
@@ -455,8 +460,8 @@ to resolve the requirements of the project with an error.
 
 !!! note
 
-    There is currently no way to declare conflicting dependency groups. See
+    If you have dependency groups that conflict with one another, resolution will fail
-    [astral.sh/uv#6981](https://github.com/astral-sh/uv/issues/6981) to track support.
+    unless you explicitly [declare them as conflicting](./projects.md#optional-dependencies).
 
 ### Default groups
 

docs/concepts/projects.md

@@ -484,10 +484,67 @@ each other and resolves all optional dependencies together when creating the loc
 If optional dependencies declared in one extra are not compatible with those in another extra, uv
 will fail to resolve the requirements of the project with an error.
 
-!!! note
+To work around this, uv supports declaring conflicting extras. For example, consider two sets of
+optional dependencies that conflict with one another:
 
-    There is currently no way to declare conflicting optional dependencies. See
+```toml title="pyproject.toml"
-    [astral.sh/uv#6981](https://github.com/astral-sh/uv/issues/6981) to track support.
+[project.optional-dependencies]
+extra1 = ["numpy==2.1.2"]
+extra2 = ["numpy==2.0.0"]
+```
+
+If you run `uv lock` with the above dependencies, resolution will fail:
+
+```console
+$ uv lock
+  x No solution found when resolving dependencies:
+  `-> Because myproject[extra2] depends on numpy==2.0.0 and myproject[extra1] depends on numpy==2.1.2, we can conclude that myproject[extra1] and
+      myproject[extra2] are incompatible.
+      And because your project requires myproject[extra1] and myproject[extra2], we can conclude that your projects's requirements are unsatisfiable.
+```
+
+But if you specify that `extra1` and `extra2` are conflicting, uv will resolve them separately.
+Specify conflicts in the `tool.uv` section:
+
+```toml title="pyproject.toml"
+[tool.uv]
+conflicts = [
+    [
+      { extra = "extra1" },
+      { extra = "extra2" },
+    ],
+]
+```
+
+Now, running `uv lock` will succeed. Note though, that now you cannot install both `extra1` and
+`extra2` at the same time:
+
+```console
+$ uv sync --extra extra1 --extra extra2
+Resolved 3 packages in 14ms
+error: extra `extra1`, extra `extra2` are incompatible with the declared conflicts: {`myproject[extra1]`, `myproject[extra2]`}
+```
+
+This error occurs because installing both `extra1` and `extra2` would result in installing two
+different versions of a package into the same environment.
+
+The above strategy for dealing with conflicting extras also works with dependency groups:
+
+```toml title="pyproject.toml"
+[dependency-groups]
+group1 = ["numpy==2.1.2"]
+group2 = ["numpy==2.0.0"]
+
+[tool.uv]
+conflicts = [
+    [
+      { group = "group1" },
+      { group = "group2" },
+    ],
+]
+```
+
+The only difference with conflicting extras is that you need to use `group` instead of `extra`.
 
 ## Managing dependencies