Log MCPServer handler exceptions by kind and keep crash details off the wire #4060

Job	Run time
checks / pre-commit	55s
checks / docs	1m 39s
checks / readme-snippets	12s
checks / test (3.10, locked, ubuntu-latest)	1m 30s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 8s
checks / test (3.10, lowest-direct, windows-latest)	1m 37s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 32s
checks / test (3.10, locked, windows-latest)	2m 14s
checks / test (3.12, locked, windows-latest)	2m 11s
checks / test (3.11, lowest-direct, ubuntu-latest)	1m 27s
checks / test (3.14, lowest-direct, windows-latest)	1m 47s
checks / test (3.13, locked, windows-latest)	1m 57s
checks / test (3.12, lowest-direct, windows-latest)	2m 16s
checks / test (3.12, locked, ubuntu-latest)	1m 45s
checks / test (3.14, locked, windows-latest)	2m 9s
checks / test (3.11, locked, ubuntu-latest)	1m 26s
checks / test (3.11, lowest-direct, windows-latest)	2m 1s
checks / test (3.13, lowest-direct, windows-latest)	2m 1s
checks / test (3.13, lowest-direct, ubuntu-latest)	1m 24s
checks / test (3.13, locked, ubuntu-latest)	1m 19s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 43s
checks / test (3.11, locked, windows-latest)	2m 0s
checks / test (3.14, locked, ubuntu-latest)	1m 27s
all-green	5s
	37m 45s

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