This already works with a few steps.
RunGap can be connected to Dropbox, where it creates two folders, import, and export.
TrainerDay can already connect to Dropbox, though as I see it you can not select custom or multiple folders yet.
Until then you can use this: Dropbox to Dropbox Sync - IFTTT or another automation process to copy files from the Dropbox Trainerday folder to the Dropbox RunGap Import folder.
After that you can manually or automatically upload your Trainerday finished workouts to Garmin, via RunGap. You can even spoof the file, so Garmin thinks it comes from a Garmin device and you can therefore earn badges, etc.
@Alex there is one problem though, some files are not correctly formatted, 0’s in the file, aka speed and distance not working like on intervals not long ago - could be only old files, as some newer ones seem to have the data.
Did you fix your files or was the fix only made on intervals.icu?