feat(client): store InitializeResult as initialize_result #1526

Job	Run time
checks / test (3.13, lowest-direct, ubuntu-latest)	52s
checks / test (3.10, locked, ubuntu-latest)	53s
checks / test (3.10, lowest-direct, windows-latest)	2m 22s
checks / test (3.13, lowest-direct, windows-latest)	2m 18s
checks / test (3.11, locked, windows-latest)	2m 15s
checks / test (3.10, lowest-direct, ubuntu-latest)	54s
checks / test (3.12, lowest-direct, windows-latest)	3m 36s
checks / test (3.11, lowest-direct, ubuntu-latest)	55s
checks / test (3.12, locked, ubuntu-latest)	51s
checks / test (3.11, lowest-direct, windows-latest)	2m 24s
checks / test (3.12, locked, windows-latest)	2m 54s
checks / test (3.12, lowest-direct, ubuntu-latest)	56s
checks / test (3.11, locked, ubuntu-latest)	55s
checks / test (3.10, locked, windows-latest)	2m 4s
checks / test (3.13, locked, ubuntu-latest)	49s
checks / pre-commit	34s
checks / test (3.14, locked, ubuntu-latest)	2m 20s
checks / test (3.14, lowest-direct, windows-latest)	2m 28s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 11s
checks / test (3.13, locked, windows-latest)	2m 11s
checks / test (3.14, locked, windows-latest)	2m 55s
checks / readme-snippets	12s
all-green	4s
	36m 53s

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