Pseudobulk after Performing integration with scatlasvae or scVI?

Hey everyone, I have integrated my dataset with CD8 dataset Integrative mapping of human CD8+ T cells in inflammation and cancer | Nature Methods, and it integration looks good.
I was interested in performing pseudobulk analysis. Would it be possible?
I saw another post discussing something similar on the same line, but i did not get the conclusion.

I ran decoupler after integration, but it looks like the batch effect is evident on the PCA plot.
How to go about it?

Blue cells are the ones that were integrated.

Thanks in Advance !

how does the plot look after scvi (and not pca) integration?

You can use the sc.pp.pseudobulk function from decoupler to generate an expression matrix for pseudobulk analysis, then perform differential analysis with PyDESeq2. During the differential analysis, specify the batch information you want to correct for as covariates. The differential analysis uses count data and is unrelated to methods like SCVI that do not alter the numerical values of the expression matrix.

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the integration looks fine. The data integrated quite well.

Yup that’s what i read. However, I am bit confused how to interpret the PCA data ?
If you go by the PCA this looks like strong batch effect.