I can not trust (yet) in the Advanced Digitizing panel as a CAD tool.
I take all possible precautions, drawing near the origin of coordinates of my custom CRS, all measures setted to planimetric, same CRS for the project and the layer, also without reprojecting on-the-fly (without project CRS), and when I want to draw a line of 20 meters perpendicular to another, it is labeled, i.e. 20.0000000000145 meters. The difference varies according to the angles I use, also varies if I am not near the origin of coordinates, wich makes me doubt about the planimetric concept.
In the update of this answer: Deleting all lines not perpendicular to another line layer using QGIS?, I found that I could not select two perpendicular lines when they were digitized as perpendicular with the Advanced Digitizing panel, until I round the azimuths by 5 decimal places.
About the circles, must be digitized in a compatible with curves data provider. Temporary scratch layer accepts compound curves, so it is a good option. But then the snap tool does not find the intersection. Your method of the Lines intersections tool seems to me a good approach.
When the snap tool finds the intersection within two curves, they are not such thing.
So, the answer is:
If you are fine with the tolerances of the Advanced Digitizing tool for the angles, distances, and/or coordinates, just draw the circles in a temporary scratch layer, find the Line intersections and snap to that points.