Fix bugs in `cylc broadcast` #6819

Job	Run time
1/4	13m 25s
2/4	17m 40s
3/4	18m 23s
4/4	15m 13s
py-3.11	15m 28s
flaky	7m 13s
_remote_background_indep_poll	5m 31s
_remote_background_indep_tcp	7m 37s
macos 1/5	21m 55s
macos 2/5	21m 42s
codecov	16s
	2h 24m 23s

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