Welcome @ginghis!
Trimming circles can be indeed cumbersome.
Not only for the user, for developers too. There are so many special cases with trimming circles that it is hard to program a clean solution and it is not always obvious what happens.
Also, the entity changes from a circle to an arc with trimming, which are completely different types in the sense of DXF representation.
That said, have a look at my link above, if you haven't already. There I explained trimming an arc.
When I have to trim a circle I usually use the divide tool with snap to intersection. I divide the circle at the needed arc endpoints and delete the rest. This method works best for me, without any surprises.
Your attached drawing is an auto saved backup file and does not contain small circles as you mentioned. So I can't provide more detailed instructions.
Armin
investing less than half an hour into Search function can save hours or days of waiting for a solution