docs: add server-side tool error handling documentation #4218

Job	Run time
checks / doc-snippets	11s
checks / pre-commit	27s
checks / test (3.10, lowest-direct, ubuntu-latest)	46s
checks / test (3.12, highest, ubuntu-latest)	46s
checks / test (3.11, lowest-direct, ubuntu-latest)	42s
checks / test (3.10, lowest-direct, windows-latest)	2m 13s
checks / test (3.13, highest, windows-latest)	2m 27s
checks / test (3.12, highest, windows-latest)	3m 19s
checks / test (3.12, lowest-direct, windows-latest)	3m 33s
checks / test (3.12, lowest-direct, ubuntu-latest)	54s
checks / test (3.11, lowest-direct, windows-latest)	2m 31s
checks / test (3.10, highest, ubuntu-latest)	52s
checks / test (3.11, highest, ubuntu-latest)	43s
checks / test (3.13, lowest-direct, windows-latest)	2m 24s
checks / test (3.11, highest, windows-latest)	2m 32s
checks / test (3.13, highest, ubuntu-latest)	53s
checks / test (3.13, lowest-direct, ubuntu-latest)	49s
checks / test (3.10, highest, windows-latest)	2m 19s
all-green	3s
	28m 24s

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