raise without from discards exception chain in 12 remaining sites

Initial Checks

• I confirm that I'm using the latest version of MCP Python SDK
• I confirm that I searched for my issue in https://github.com/modelcontextprotocol/python-sdk/issues before opening this issue

Description

Follow-up to #2541 (fixed in #2542). The same pattern exists in 12 additional sites across 7 files. Each catches an exception and re-raises a new one without from, discarding the original traceback and __cause__.

Sites:

Impact

Same as #2541: without from, Python shows "During handling of the above exception, another exception occurred" instead of "The above exception was the direct cause of the following exception." Callers cannot inspect __cause__ to determine the root cause programmatically.

The codebase already uses from correctly in server.py:451, server.py:459, server.py:1112, func_metadata.py:216,265, and tools/base.py:119. These 12 sites are the remaining inconsistencies.

Start by inspecting the 12 listed sites in client/session.py, client/auth/utils.py, server/auth/middleware/client_auth.py, server/mcpserver/resources/types.py, resource_manager.py, templates.py, and prompts/base.py. Compare them with the existing uses in server.py, func_metadata.py, and tools/base.py. Done means each re-raised exception preserves the original as its direct cause and the relevant client and server behavior remains passing.