I have 4 biological replicates of mRNA samples. For my dds, I am comparing type but have also added in the replicate factor to account for the biological replicates.

Is this correct? I have a column specifying the replicate number (1, 2, 3, or 4) per sample as they do not have the same names.

dds <- DESeqDataSetFromMatrix(
  countData = counts_data,
  colData = metadata,
  design = ~ Replicate + Type  # accounting for biological replicates
)

Generally, you don't have to include the replication information since the software will consider all elements of dds$Type that have the same factor level as replicates for this group. It can sometimes make sense to include the replicate information, for example if every replicate is a different batch, so essentially replicate would be the same as batch, and there is evidence, for example in PCA, that batch is driving unwanted variation. If not, don't include.

Go read the vignette. They don't include replicate.