First, the context for CMS, NASA's Carbon Monitoring System, needs to be stated. That project web page states the goal as
NASA's CMS project is to prototype the development of capabilities necessary to support stakeholder needs for Monitoring, Reporting, and Verification (MRV) of carbon stocks and fluxes.
- Use the full range of NASA satellite observations, modeling/analysis capabilities, and commercial off-the-shelf technologies to establish the accuracy, quantitative uncertainties, and utility of products for supporting national and international policy, regulatory, and management activities.
- Prototype the development of carbon Monitoring Reporting and Verification [MRV] systems which can provide transparent data products achieving levels of precision and accuracy required by current carbon trading protocols.
It was never (just) a "program to track greenhouse gases" per se, though it would use that information as part of the overall goal.
GEDI was one of about a half-dozen missions and instruments associated with CMS. But GEDI was not an project of CMS itself; CMS was only to use the information from GEDI. The GEDI instrument is under the NASA EOS Project Science Office.
OCO-3 and NISAR are the two items on the CMS mission page that are most relevant to atmospheric CO2. They're farther out than GEDI, and the cancellation of CMS may make their (proposed) products in less demand, which may weaken their prospects. But they too are under the EOS PSO, with no formal place under CMS.
CMS did fund a number of analysis projects. The loss of those is going to be problematic for a bunch of investigators; this kind of thing can really hurt grad student careers, resulting in a kink in the pipeline for future scientists. But it's direct effect on NASA missions seems likely to be small.
Now, on the specific questions:
Other than the fact that trees contain carbon, and GEDI can confirm that the trees exist, how can GEDI be used as a carbon-monitoring or specifically a greenhouse gas measuring instrument?
GEDI will be measuring components of overall environmental carbon:
The scientific goal of the Global Ecosystem Dynamics Investigation Lidar (GEDI) is to characterize the effects of changing climate and land use on ecosystem structure and dynamics to enable radically improved quantification and understanding of the Earth's carbon cycle and biodiversity. Focused on tropical and temperate forests from its vantage point on the International Space Station (ISS), GEDI uses lidar to provide the first global, high-resolution observations of forest vertical structure. GEDI addresses three, core science questions:
(Q1) What is the aboveground carbon balance of the land surface?
(Q2) What role will the land surface play in mitigating atmospheric carbon dioxide in the coming decades?
(Q3) How does ecosystem structure affect habitat quality and biodiversity? Answering these questions is critical for understanding the future path of global climate change and the Earth’s biodiversity.
Although that doesn't specifically include greenhouse gas carbon, it's still measuring the things that CMS was going to analyze, and that data can be used for those analyses under other headings too.
Is this just Ketchup as a vegetable-speak, or does GEDI have instruments that monitor atmospheric carbon, or is there another way to look at this I'm missing?
The way to look at this is that the overall coverage of the the cancellation of CMS has given the wrong impression. By focusing on greenhouse gas, the coverage understates (or misdirects?) what CMS was doing. The NASA statement was trying to address the idea that GEDI will still be doing the (observational) part of CMS's mission, same as it ever was.
As a policy matter, the cancellation of CMS raises questions about "who's going to provide the facts for future policy adoption and implementation?" But perhaps that's a different question for a different Stack Exchange group.