I got an RNA-Seq project where the data looks like as in the PCA plot below - 4 biological replicates of 4 conditions, and there are 4 batches with each batch consisting of 1 sample from each condition. In essence the variation between biological replicates is larger than the variation in the tested conditions most likely due to batch effects. Likely the wet-lab has processed each replicate of all conditions at different days.

I was thinking to include a batch into the design formulae, but on the other hand (as far as I understand) it will "remove" the variation between biological replicates, so I was wondering if that analysis would make sense?

Any advice is much appreciated

DISCLOSURE: Cross-posted in Biostars a week ago https://www.biostars.org/p/9562841/#9563062

Your design is not confounded, you can use ~batch + condition. You will still have residual degrees of freedom because you have 16 samples and this design has 5 coefficients.