Two siblings: This doesn’t tell us much, two brothers, two sisters, a brother and a sister, what are their personalities.
Leave a miserable home: Okay, again is it the father who is mean? is it the mother who is making life difficult? Are they in an orphanage?
in the wake of the country’s civil war: Which country, the United States? France and the french revolution? Russia? Many countries have had civil wars, you should be more specific.
they embark on an austere quest: austere? I take that to mean somber. That doesn’t sound very appealing. A miserable home and a somber quest.
to find a new life in a foreign country: Which country? It would take just as many words (or less) to say England, France, Brazil than to say vaguely “A foreign country” Be specific.

Your characters should have a specific goal. A new life is not very specific.

Here would be an example of two siblings leaving their miserable home to get a new life, while using specifics: (Yours would be different, of course)
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“When their over bearing father forbids them to become rodeo clowns, two Muslim brothers fascinated?with cowboys escape war torn Syria and arrive in Dallas in the hopes of achieving their dreams of rodeo stardom.”
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We now know who they are, what they want, where they are from, who was oppressing them and where they have arrived, and can visualize the problems they may encounter.

Here is a look at the second logline example you wrote:

2. “A young Sherlock Holmes and Moriarty plan to undermine England?s holdings in the east to profit from deals in Russia, while Mycroft Holmes is tasked by MI5 find who is responsible, not knowing their involvement.“
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I like this version and would only make a small change or two
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“Master criminal Sherlock Homes and sidekick Moriarty plan to get rich by undermining England’s holdings in the east, but must outwit his genius brother, Mycroft who has been appointed by MI5 to monitor the region.”
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