perf(tui): avoid reparsing frozen streaming markdown #2912

Job	Run time
build	10s
static-analysis	48s
test (3/4)	38s
test (1/4)	1m 11s
test (2/4)	1m 3s
test (4/4)	52s
test (one-process pollution detector)	0s
eslint	3s
typecheck	4s
prettier	2s
build-and-test	4s
test (src)	2s
	4m 57s

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