Where is the verb in the sentence "Sin é mo dheartháir"? I have seen "Sin é" in other contexts where it means 'that is'. Is it understood to be 'is' so that "Sin é mo dheartháir" is really "Is sin é mo dheartháir"?

Sin é = is in é. Is is the verb (copula). You could also say Is é sin/sé sin mo dheartháir.

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I'm an intermediate speaker of the Corca Dhuibhne dialect of Irish and also have knowledge on the old spelling
Soir gaċ síar, fé ḋeireaḋ thíar

Nowadays yes. Such sentences are regarded as copula sentences, "is" is understood.
The s of sin is regarded as the copula, in other tenses and circumstances the s of sin gets lost, e.g.
in past tense, it would be B'in é mo dheartháir (That was my brother) with past tense copula ba (b'in = that was).

Thank you. That is what I assumed, but I wanted to confirm.

Sin é... = is in é, I believe. Similarly, seo... = Is eo.

I've also seen "sea" around (I think it's sensible?), sea = is ea.

And "is" is indeed the verb.