I am analyzing bulk-RNA sequencing across a hundred patients, where some patients have triplicate stem cell lines. Some of the triplicates are technical replicates (the same cell culture line was sequenced three times), while others are biological replicates (stem cells from the same patient were independently cultured and sequenced).

How should I deal with the different kinds of replicates? Should I merge all replicates or only the technical replicates? My concern with leaving the biological replicates separate is that there will be an overrepresentation of these samples since most other patients do not have biological replicates.

Technical replicates (more sequencing of same library) you can use collapseReplicates().

But biological replicates are best handled with something like a random effect. We don't support this in DESeq2, but limma has something called duplicateCorrelation -- see many support site posts on this topic.