Thanks for pointing this out, @JMichaelTX! It was quite easy getting the data from my sample Airtable DB with a curl
command in the Execute a Shell Script action as per their instructions. The only downsides that I see are that it seems to be considerably slower to get the data from the API instead of copying it to the clipboard, and the resulting data is in JSON rather than an easier-to-parse (at least for someone like me, who doesn't know much JavaScript) tab-separated variables format. The slowness may be acceptable depending on the use case, but for the second issue, it may be worth waiting until KM 9 is out, since one of the new features will be built-in parsing for JSON data.