feat(client): store InitializeResult as initialize_result #1522

Job	Run time
checks / pre-commit	39s
checks / readme-snippets	13s
checks / test (3.10, lowest-direct, ubuntu-latest)	46s
checks / test (3.10, lowest-direct, windows-latest)	2m 15s
checks / test (3.11, locked, ubuntu-latest)	39s
checks / test (3.14, locked, windows-latest)	3m 8s
checks / test (3.11, lowest-direct, windows-latest)	2m 14s
checks / test (3.13, locked, ubuntu-latest)	41s
checks / test (3.13, lowest-direct, windows-latest)	2m 17s
checks / test (3.10, locked, ubuntu-latest)	45s
checks / test (3.11, locked, windows-latest)	2m 15s
checks / test (3.11, lowest-direct, ubuntu-latest)	44s
checks / test (3.14, lowest-direct, windows-latest)	2m 27s
checks / test (3.12, locked, ubuntu-latest)	47s
checks / test (3.12, locked, windows-latest)	3m 34s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 5s
checks / test (3.13, lowest-direct, ubuntu-latest)	47s
checks / test (3.12, lowest-direct, ubuntu-latest)	52s
checks / test (3.10, locked, windows-latest)	2m 0s
checks / test (3.13, locked, windows-latest)	2m 14s
checks / test (3.12, lowest-direct, windows-latest)	3m 15s
checks / test (3.14, locked, ubuntu-latest)	2m 8s
all-green	4s
	35m 49s

Provide feedback