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I can't find the exact type and settings for the BLS12-381 curve.

Is this type-3 in Symmetric XDH settings ?

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BLS12-381 is a Type 3 curve, yes. I'm not aware of any difficulty of assuming SXDH for BLS12 curves, and there's no reason BLS12-381 in particular would be special in this respect.

(Almost all pairing-based protocols defined recently are designed for Type 3 curves, and almost all curves defined recently for pairing-based crypto are Type 3. If you come across anything else, it's probably quite an old protocol or curve that hasn't taken into account later cryptographic developments, and you should be quite suspicious of that.)

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