docs: clarify update-artifact wording (DOCS-1215) (#2329)

## Summary

Updates [Update an
artifact](https://docs.wandb.ai/models/artifacts/update-an-artifact) to
avoid vague "inside/outside a run" language. The page now contrasts
**while a run is active** with **Public API only** (no `wandb.init()`),
renames the second tab accordingly, and tightens the intro and guidance
paragraphs.

## Test plan

- [ ] `mint broken-links` (optional)
- [ ] Spot-check the page in Mintlify preview

Resolves DOCS-1215

Made with [Cursor](https://cursor.com)

---------

Co-authored-by: Noah Luna <15202580+ngrayluna@users.noreply.github.com>

Author: johndmulhausen

models/artifacts/update-an-artifact.mdx

@@ -1,18 +1,18 @@
 ---
-description: Update an existing Artifact inside and outside of a W&B Run.
+description: Update an existing artifact while a run is active or using only the Public API.
 title: Update an artifact
 ---
 
-Pass desired values to update the `description`, `metadata`, and `alias` of an artifact. Call the `save()` method to update the artifact on the W&B servers. You can update an artifact during a W&B Run or outside of a Run.
+Pass desired values to update the `description`, `metadata`, and `alias` of an artifact. Update a run previously logged to W&B with the W&B Public API with ([`wandb.Api`](/models/ref/python/public-api/api)). Use `wandb.Run.save()` to update an artifact when is first initialized and still active. 
 
 <Note>
-**When to use Artifact.save() or wandb.Run.log_artifact()**
+**When to use wandb.Artifact.save() or wandb.Run.log_artifact()**
 
-- Use `Artifact.save()` to update an existing artifact without creating a new run.
+- Use `Artifact.save()` to update an existing artifact without starting a new run.
 - Use `wandb.Run.log_artifact()` to create a new artifact and associate it with a specific run.
 </Note>
 
-Use the W&B Public API ([`wandb.Api`](/models/ref/python/public-api/api)) to update an artifact outside of a run. Use the Artifact API ([`wandb.Artifact`](/models/ref/python/experiments/artifact)) to update an artifact during a run.
+Use the W&B Public API ([`wandb.Api`](/models/ref/python/public-api/api)) to update an artifact. Use the wandb.Artifact ([`wandb.Artifact`](/models/ref/python/experiments/artifact)) Class while a run is active.
 
 <Warning>
 You can not update the alias of artifact linked to a model in Model Registry.
@@ -31,8 +31,8 @@ with wandb.init(project="<example>") as run:
     artifact.save()
 ```
 </Tab>
-<Tab title="Outside of a run">
-The following code example demonstrates how to update the description of an artifact using the `wandb.Api` API:
+<Tab title="W&B Public API">
+The following example updates an artifact with [`wandb.Api`](/models/ref/python/public-api/api):
 
 ```python
 import wandb