Thanks for your reply.
I understand that genes in the purified sample are not 'upregulated', but they are enriched compared to input RNA. Using differential expression analysis is what others have performed to identify which genes are translated in the target cell type (for example: Epigenetic regulation of brain region-specific microglia clearance activity). My concern is whether the normalisation is appropriate to check for gene enrichment.
The main objective of my work is to compare the purified samples across conditions, where I can assume that the RNA composition is similar. As you say, I will also compare the input RNA between conditions to then show how condition-dependent DEGs differ between the purified and input samples.