As ATpoint already said, above, first make sure all the standard QC steps (including, but not limited to, gene-level QC (e.g. prefiltering) and sample-level QC (e.g. sample distance matrix visualization & PCA plot generation to identify outlying samples, in particular samples that lie far from other samples in the same group(s)) are solid. All of that is covered in the vignette as I expect you already know.
Assuming this has been done, you've already taken what I think is likely the next most important step, i.e., identify commonalities between the markers that cluster in the log2FC high group you seem to be referring to.
For this MA plot, I might isolate all logFCs greater than 2.5, but less than 4, then pull the gene symbols for these. Next, I'd enter that list of gene symbols into a tool like DAVID, to see if they have any biologic coherence. If these genes are known to be co-expressed in physiologic states (here, apoptosis), and if the co-expression relationships mimic what can be observed in other apoptotic cells of similar type, it's more likely a real finding...
The problem is, in this case, apoptosis is a tricky state in this regard. Lots of machinery that can affect RNA-seq results is activated, including mechanisms to destroy RNA as well as changes to cell permeability, for instance. As a result, I'd want to know exactly why these genes are LFC up, and what exactly they have to do with apoptosis. As an example, consider: are they LFCup because they are NOT being degraded in non-apoptotic samples, or are they LFCup because they are upregulated in apoptotic samples. To do this, could consider generating countPlots of genes you understand very well, then sanity checking that the direction of effect makes sense and is consistent with the known biology displayed by "normal" intact cells of that type beginning apoptosis...
For these reasons, I do think you are right to be cautious. While I've seen many examples where far more genes are LFCup than LFCdown, or the reverse, I have never seen a case quite like this before. Finally, you can also expect to get a question like this from a reviewer if you include the MAplot. So, irrespective I'd make it a point to control for the batches you indicate and to be able to defend the results.
What happens when you remove the SVA covariates?
I did rund DESeq2 without surrogate variables, the MA-plot abnormalities were still present.
Exvessive logFC with low baseMean is usually due to poor or no prefiltering. I personally find rowsum/rowmean-based filtering suboptimal. Do it group-aware, see for example https://support.bioconductor.org/p/9152700/#9152701
Thanks for your input! I will definetly look into that. But as you can see from the MA plot, not only low baseMean genes are affected here. Hence I don't think I'll be able to get rid of this just by adjusting the pre-filter.