They report on the investigations as part of their papers looking at the safety of each vaccine, which often breaks down to various demographics.

For instance, here is the monthly report for the Johnson & Johnson vaccine.

Under Review of VAERS Data, it describes the further investigations:

CDC and FDA reviewed 88 reports of death after receipt of Janssen COVID-19 vaccine; death certificates were available for 12 (14%). Among the 88 reported decedents, 44 were female, 38 were male, and the sex of six was not reported (Table 1). The median decedent age was 69 years (range = 21–97 years); median interval from vaccination to death was 2 days (range = 0–23 days). All death reports received a medical review§§§; the most frequent preliminary impressions of CDC and FDA reviewers regarding cause of death were 1) decedent found dead, with no additional details available (34 reports); 2) cardiac arrest or cardiovascular disease (23 reports); 3) COVID-19 disease (eight reports); and 4) cerebrovascular disease (five reports). As of most recent follow-up (April 28, 2021), three patients with TTS had died. Among 79 reports of anaphylaxis after vaccination, four were confirmed as anaphylaxis cases after interview with a health care provider or review of medical records (<0.5 cases per 1 million doses administered); four reports remain under review. Headache (34%), fever (34%), chills (33%), injection site pain (26%), and fatigue (24%) were the symptoms most frequently reported to VAERS (Table 1).

The weekly MMWR put out by the CDC includes findings from the investigation of deaths in the VAERS system.