I'm not familiar with the new syllabus but I can tell you how it was in the older syllabus.

In the older syllabus, circle geometry problems were pretty limited in scope - some diagram involving circles is given and you have to bash out those circle geo-specific theorems you memorised to prove a relationship between some angles and lines.

The geometry problems outside of the circle geo topic rarely involved circles at all, usually either polygons and/or lines, or other conic sections (parabola, hyperbola, ellipse). They generally favoured algebraic approaches as well. If a circle was involved there wasn't too much going on with it - it's not often you need to deal with angles inscribed inside circles or subtended by chords.

So, the circle geo theorems were basically only useful for circle geo questions. There wasn't much overlap between circle geometry and other geometry.

(But as always, one thing that does carry over is the development of mathematical skills in solving problems.)