feat(client): store InitializeResult as initialize_result #1510

Job	Run time
checks / readme-snippets	11s
checks / pre-commit	33s
checks / test (3.10, locked, windows-latest)	2m 18s
checks / test (3.11, locked, ubuntu-latest)	55s
checks / test (3.10, lowest-direct, windows-latest)	2m 37s
checks / test (3.11, lowest-direct, ubuntu-latest)	53s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 3s
checks / test (3.12, locked, windows-latest)	3m 29s
checks / test (3.12, locked, ubuntu-latest)	59s
checks / test (3.10, locked, ubuntu-latest)	52s
checks / test (3.10, lowest-direct, ubuntu-latest)	55s
checks / test (3.12, lowest-direct, windows-latest)	3m 44s
checks / test (3.11, lowest-direct, windows-latest)	3m 34s
checks / test (3.14, locked, ubuntu-latest)	2m 20s
checks / test (3.11, locked, windows-latest)	2m 33s
checks / test (3.13, lowest-direct, windows-latest)	2m 43s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 13s
checks / test (3.13, locked, ubuntu-latest)	50s
checks / test (3.14, locked, windows-latest)	3m 12s
checks / test (3.14, lowest-direct, windows-latest)	2m 20s
checks / test (3.13, lowest-direct, ubuntu-latest)	54s
checks / test (3.13, locked, windows-latest)	2m 18s
all-green	2s
	40m 28s

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