Disclaimer: I am an interested amateur and there may be mistakes in what I write here.
There are good explanations of the science (by Firstbeat technologies which is used by Garmin) behind these stats: https://www.firstbeat.com/en/science-and-physiology/
Training Status is based on VO2Max and training load over time: "Training Status analyzes the patterns in your VO2max and Training Load history" VO2Max is based on "measurement of running speed along with heart rate":
"Firstbeat Analytics can automatically detect your VO2max fitness level during walking and running activities [..] The calculation relies on a combination of personal background information and data collected during your activity. This includes a focus on heart rate and running/walking speed"
From this it is not clear if they use heart rate variability or beats per minute, but I suppose HRV (BPM has less resolution, you can calculate BPM from HRV, but not the other way around), and their paper on VO2Max mentions that too: "this white paper has been produced to review the method and empirical results related to the heart rate variability and speed based VO2max estimation method from any freely performed workout developed by FirstbeatTechnologies Ltd."
These algorithms are real good at filtering out only valid data. If your HRM is not giving enough valid data for long enough (static interference from rubbing clothes, worn out electrode pads, battery is near empty, or not worn tight enough) too much may be thrown out.
Heart rate variability is based on the intervals between each heartbeat (R-R intervals) in milliseconds. Basically what each HRM measures. But.. activities I do with an old optical HRM do not contain HRV data, only BPM. I'm not sure if that old HRM sends it or not. See the ANT+ device profile HRM for more information.
You could have a look at the HRV data itself (BPM heart rate graph won't show the outliers in the data) and visually inspect how it, if it has many outliers or is stuck on one value for a long time. Not sure if Garmin Connect can do that, but Runalyze is one of the online tools that can.
Other ways to get rubbish stats: I get those for example when it is very windy: struggling, HR high, but slow going.