Both the Slavic brat (Брат) and the Latin frater mean brother.
Are they cognates? Or is their phonetic "proximity" a red herring?
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Yes, frater and Брат are related.
They ultimately come from the Proto-Indo-European *bʰréh₂tēr, from which indeed brat/Брат in various Slavic languages also is derived. You can see the descendants on Wiktionary. In Latin, the PIE initial bʰ- regularly yielded f-. Another example is the PIE *bʰer-, which yields bear in English and ferre in Latin.
It's certainly good to question whether two words are "false cognates", as plenty of words in languages can look the same but come from entirely separate origins. In this case, though, the various words for "brother" in Proto-Indo-European languages is actually clear cut.
As far as Wiktionary goes, it is generally reliable, but you can always check a Latin etymological dictionary like De Vaan's if you're unsure.