feat(client): store InitializeResult as initialize_result #1506

Job	Run time
checks / pre-commit	32s
checks / readme-snippets	12s
checks / test (3.11, locked, windows-latest)	2m 34s
checks / test (3.11, lowest-direct, ubuntu-latest)	57s
checks / test (3.10, locked, windows-latest)	2m 23s
checks / test (3.10, lowest-direct, windows-latest)	2m 40s
checks / test (3.12, locked, ubuntu-latest)	56s
checks / test (3.14, locked, windows-latest)	3m 17s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 1s
checks / test (3.11, locked, ubuntu-latest)	51s
checks / test (3.13, lowest-direct, ubuntu-latest)	53s
checks / test (3.12, lowest-direct, windows-latest)	3m 51s
checks / test (3.12, locked, windows-latest)	4m 0s
checks / test (3.13, locked, ubuntu-latest)	48s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 24s
checks / test (3.14, locked, ubuntu-latest)	2m 49s
checks / test (3.10, lowest-direct, ubuntu-latest)	56s
checks / test (3.13, locked, windows-latest)	2m 28s
checks / test (3.14, lowest-direct, windows-latest)	2m 35s
checks / test (3.13, lowest-direct, windows-latest)	2m 52s
checks / test (3.10, locked, ubuntu-latest)	53s
checks / test (3.11, lowest-direct, windows-latest)	2m 57s
all-green	2s
	41m 51s

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