Store server_info on ClientSession during initialization #369

Job	Run time
checks / pre-commit	32s
checks / readme-snippets	11s
checks / test (3.11, lowest-direct, ubuntu-latest)	55s
checks / test (3.10, lowest-direct, ubuntu-latest)	51s
checks / test (3.10, locked, ubuntu-latest)	46s
checks / test (3.10, locked, windows-latest)	2m 23s
checks / test (3.11, lowest-direct, windows-latest)	2m 37s
checks / test (3.11, locked, windows-latest)	2m 29s
checks / test (3.14, lowest-direct, windows-latest)	2m 24s
checks / test (3.13, locked, windows-latest)	2m 32s
checks / test (3.13, lowest-direct, windows-latest)	3m 7s
checks / test (3.12, locked, windows-latest)	3m 22s
checks / test (3.12, lowest-direct, windows-latest)	3m 29s
checks / test (3.10, lowest-direct, windows-latest)	2m 34s
checks / test (3.12, locked, ubuntu-latest)	51s
checks / test (3.14, locked, ubuntu-latest)	2m 22s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 16s
checks / test (3.11, locked, ubuntu-latest)	46s
checks / test (3.13, locked, ubuntu-latest)	50s
checks / test (3.13, lowest-direct, ubuntu-latest)	51s
checks / test (3.14, locked, windows-latest)	3m 59s
checks / test (3.12, lowest-direct, ubuntu-latest)	49s
all-green	3s
	39m 59s

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