Are there any viruses that integrate their DNA into organellar DNA?
I'm only aware of one paper that claims to show regular viral integration into mitochondrial DNA, and even there they suggest it might be a host defense rather than a viral life cycle thing:

Interestingly, 69.4% (50/72) of HBV integration sites were observed in human mitochondrial DNA (mtDNA) (Supplementary Table 2). ... However, 32% of HBV integration sites in mtDNA (16/50) were in the displacement loop (D-loop) region, which is known as the major control site for mtDNA expression as it contains the origin of replication for the heavy DNA strand and the major promoters of transcription (Figure 1B). Of note, we repeatedly detected mtDNA integration events through the same micro-homology site in independent mice, indicating the hotspot for HBV integration in mtDNA, which is probably related to replication or transcription. ...
We found that HBV integrations were mediated through MMEJ, which is known as an alternative DNA double-strand break (DSB) repair system and reported as a principal mediator during mitochondrial DNA lesions. This suggests that early-phase HBV integration occurred in mtDNA. Damage in mtDNA is known to induce autophagy and was removed in C. elegans, therefore it is possible that integration of HBV DNA into mtDNA might be a defensive mechanism to protect the nucleus from HBV integration.

--Characterization of HBV integration patterns and timing in liver cancer and HBV-infected livers
I would like to see this replicated and extended before I spent too much time wondering about functions and mechanisms.