[Core] Update changelog (#45230)

Signed-off-by: Paul Van Eck <paulvaneck@microsoft.com>

Author: pvaneck

sdk/core/azure-core/CHANGELOG.md

@@ -1,17 +1,11 @@
 # Release History
 
-## 1.38.2 (Unreleased)
-
-### Features Added
-
-### Breaking Changes
+## 1.38.2 (2026-02-18)
 
 ### Bugs Fixed
 
 - Fixed `PipelineClient.format_url` to preserve the leading slash when the URL template starts with `/?`. #45218
 
-### Other Changes
-
 ## 1.38.1 (2026-02-10)
 
 ### Bugs Fixed