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Keep the live Context when a prompt or template annotates Context[T] … #4426

Job	Run time
checks / docs	1m 41s
checks / pre-commit	43s
checks / test (3.14, locked, windows-latest)	2m 12s
checks / test (3.11, lowest-direct, ubuntu-latest)	1m 4s
checks / test (3.13, lowest-direct, windows-latest)	2m 30s
checks / test (3.14, locked, ubuntu-latest)	1m 27s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 32s
checks / readme-snippets	14s
checks / test (3.12, lowest-direct, windows-latest)	2m 15s
checks / test (3.11, locked, windows-latest)	2m 14s
checks / test (3.12, locked, ubuntu-latest)	1m 56s
checks / test (3.10, locked, windows-latest)	2m 29s
checks / test (3.13, locked, ubuntu-latest)	1m 8s
checks / test (3.13, lowest-direct, ubuntu-latest)	1m 23s
checks / test (3.11, locked, ubuntu-latest)	1m 35s
checks / test (3.10, locked, ubuntu-latest)	1m 32s
checks / test (3.13, locked, windows-latest)	2m 1s
checks / test (3.10, lowest-direct, windows-latest)	2m 16s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 41s
checks / test (3.14, lowest-direct, windows-latest)	2m 21s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 27s
checks / test (3.12, locked, windows-latest)	2m 31s
checks / test (3.11, lowest-direct, windows-latest)	1m 38s
all-green	5s
	39m 55s