[Core] Prep release (#41876)

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

Author: pvaneck

sdk/core/azure-core/CHANGELOG.md

@@ -1,6 +1,6 @@
 # Release History
 
-## 1.35.0 (Unreleased)
+## 1.35.0 (2025-07-02)
 
 ### Features Added
 
@@ -10,10 +10,6 @@
 - Added `is_generated_model` method to `azure.core.serialization`. Returns whether a given input is a model from one of our generated sdks. #41445
 - Added `attribute_list` method to `azure.core.serialization`. Returns all of the attributes of a given model from one of our generated sdks. #41571
 
-### Breaking Changes
-
-### Bugs Fixed
-
 ### Other Changes
 
 - A timeout error when using the `aiohttp` transport (the default for async SDKs) will now be raised as a `azure.core.exceptions.ServiceResponseTimeoutError`, a subtype of the previously raised `ServiceResponseError`.