The creation of weighted limits by the forgetful functor from the $\mathscr V$-category of algebras for an enriched (relative) monad is proven in Proposition 2.5 of Arkor–McDermott's Relative monadicity. I'm not aware of a reference for the creation of colimits.
The creation of bilimits by the forgetful pseudofunctor for a pseudomonad is proven in Theorem 6.3.1.6 of Osmond's A categorical study of spectral dualities. (The creation of conical bicolimits that are preserved by the pseudomonad is also claimed in Lemma 2.7 of Osmond's Codescent and bicolimits of pseudo-algebras without proof.)
varkor
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