[Backport release-3_40] [annotations] Fix non-HTML formatted annotations losing content on settings change #36712

Job	Run time
build (24.04, 5, true, OFF, ON, ON, ON, ON, OFF, OFF, OFF, OFF, ON, false)	23m 4s
build (39, 6, true, ON, OFF, ON, ON, OFF, OFF, ON, ON, ON, OFF, false)	30m 1s
Run tests (5, ALL_BUT_PROVIDERS)	28m 40s
clang-tidy (24.04, 5)	4m 56s
Run tests (5, POSTGRES)	5m 54s
Run tests (5, HANA)	5m 20s
Run tests (6, ALL_BUT_PROVIDERS)	36m 6s
Run tests (5, ORACLE, 24.04, binary-for-oracle)	6m 15s
	2h 20m 16s

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