Try using routeCourse for importing route files.
Similar issue here. GPX in NewFiles do work. TCX do not
.fit files also work in the NewFiles Folder.
To import TCX you can import the file to Garmin Connect as a course either in the web version or in the smartphone app (file explorer, tab on the file and select "open with" Garmin connect). Then you can send the course via Bluetooth to the watch. Advantage of this method is that GC adds turn by turn alerts automatically, which works quite well but not 100%.
The reason of using TCX and not GPX is to embeed custom waypoints along the route (water spots, highlights,...). This works in my Garmin Edge 830.
Unfortunately, if I import the TCX into Garmin Connect, the embeeded waypoints go away.
I never tried this because I only used turn by turn alerts so far, but I understand that for some purposes it might be helpful to have the next water/food supply as the next waypoint. Apart from .gpx also. fit files work from the newfiles folder. Did you try this? Some apps are able to export such files like Locus Maps (Android), otherwise the old Garmin Training Center might help.
So far I found only two ways to achieve embebed waypoints: Garmin Connect ("add course point" function) and QMapShack, which just embeds all your custom waypoints that are close enough to the course in the same project. Unfortunately QMapShack does not export to FIT :-)