It doesn't matter what planner is used. All the planners produce the same sort of file.

A link to the course and an indication of exactly where the problem is occurring might be useful.

for example, on this course it happened : https://connect.garmin.com/modern/course/42411639

error 1: at point A, instead of going straight, the GPS took me around the pond. When I came back to point A, it directed me again to the left. When I went straight ahead, it then recalculated the guidance and found the correct path.

This is the resulting recorded path:

Point A is:

50.590276, 3.131387

second example on this course: connect.garmin.com/.../43159483

error 2: here at point A I decided to try to lengthen the route, so I went straight instead of following the route to the left. At point B I realized that it was going far from my original direction, so I turned back. The GPS recalculated the guidance, but when I got to point C, instead of making me turn right to get back to the original route, it told me to turn left.

As I remembered the route, I "forced" the guide by turning right and he recalculated the right path afterwards.
So the recording is as follows:

If you let the unit recalculate after going off course it won't route you back onto the original course.  It will recalculate a new route to the end point of the original course.  This is highly unlikely to follow your planned route.  This has been the navigation behaviour in all Garmin head units up to the 530/830.

The new 1030 plus unit has different recalculation options that are supposed to route you back onto your original course after going off it.  This feature has not been brought to any other unit.

In example one maybe the change in surface type of the ways (road to the gravel path) confused the routing?

ah, that's a lead to check. Do you think that the fact that I'm with the "road" activity profile makes the calculator "prevent" me from going on dirt roads as much as possible? If I choose the mountain bike profile will it behave differently?
Nevertheless, when I ask to follow a track, I expect the GPS to actually make me follow the track. I don't give it a destination and leave it the choice of guidance, I WANT to follow a route that I have decided to follow

In example 2, I was back on the track and the calculator wanted to make me turn in the wrong direction. Yet the course has a direction of travel, it should have taken this into account ...

If you have let the unit recalculate then it doesn't matter if you get back on the original track as the unit is not following it any more, it has made its own route to the end point of your original route.  This is why the recommendation is to never let the unit recalculate the route and get yourself back on the route and then the unit will notice and start giving you the expected directions again.

You don't have to switch to the MTB profile to allow gravel trails.  Go in to the navigation settings for the road profile and modify adjust the avoidance setup.