245e causal ὥς?

ὡς ταύτης οὔσης φύσεως ψυχῆς:
Is this ὥς causal?

Yes surely, prefacing the genitive absolute, as often. It’s striking (especially after all the preceding neuters) how ταύτης οὔσης is attracted into the gender of φύσεως.

I take it that the “this” is the thing ᾧ ἔνδοθεν (τὸ κινεῖσθαι) αὐτῷ ἐξ αὑτοῦ, the thing whose movement is from within, itself from itself (αυτῳ εξ αὑτου)—and hence ensouled.

thank you, I should have noticed the attraction.