Add process.uptime to metrics docs

docs/system/process-metrics.md

@@ -30,6 +30,7 @@ metrics](/docs/runtime/README.md#metrics).
   - [Metric: `process.open_file_descriptor.count`](#metric-processopen_file_descriptorcount)
   - [Metric: `process.context_switches`](#metric-processcontext_switches)
   - [Metric: `process.paging.faults`](#metric-processpagingfaults)
+  - [Metric: `process.uptime`](#metric-processuptime)
 
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@@ -477,5 +478,40 @@ This metric is [recommended][MetricRecommended].
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+### Metric: `process.uptime`
+
+This metric is [recommended][MetricRecommended].
+
+<!-- semconv metric.process.uptime(metric_table) -->
+<!-- NOTE: THIS TEXT IS AUTOGENERATED. DO NOT EDIT BY HAND. -->
+<!-- see templates/registry/markdown/snippet.md.j2 -->
+<!-- prettier-ignore-start -->
+<!-- markdownlint-capture -->
+<!-- markdownlint-disable -->
+
+| Name     | Instrument Type | Unit (UCUM) | Description    | Stability |
+| -------- | --------------- | ----------- | -------------- | --------- |
+| `process.uptime` | Counter | `s` | The time the process has been running. | ![Experimental](https://img.shields.io/badge/-experimental-blue) |
+
+
+<!-- markdownlint-restore -->
+<!-- prettier-ignore-end -->
+<!-- END AUTOGENERATED TEXT -->
+<!-- endsemconv -->
+
+<!-- semconv metric.process.uptime(full) -->
+<!-- NOTE: THIS TEXT IS AUTOGENERATED. DO NOT EDIT BY HAND. -->
+<!-- see templates/registry/markdown/snippet.md.j2 -->
+<!-- prettier-ignore-start -->
+<!-- markdownlint-capture -->
+<!-- markdownlint-disable -->
+
+
+<!-- markdownlint-restore -->
+<!-- prettier-ignore-end -->
+<!-- END AUTOGENERATED TEXT -->
+<!-- endsemconv -->
+
+
 [DocumentStatus]: https://opentelemetry.io/docs/specs/otel/document-status
 [MetricRecommended]: /docs/general/metric-requirement-level.md#recommended