Trace it manually. That means redraw it, but have the original as locked in the bottom for reference
It's useless to fight with Inkscape's automatic tracing if you expect easily editable result. Inkscape traces even thinnest lines as filled areas, never as simple strokes. In addition the number of generated nodes is often frightening high as you have seen. You have no control how the shape is divided to parts except by tracing the shape several times in differently partially erased or recolored versions. This preparation must be done in a photo editor.
If you redraw it Use different colors for different parts. It's up to you to decide which parts should be separate. If you can assume the shape is LR-symmetric, you can well draw only half of it and combine the halves
Be informed that practicing a little with the Pen and the Node tool will pay the used time back generously, probably with 10000% interest.
Use preset shapes such as circles, rounded polygons etc where possible. You can combine them with path operations and edit them with the node tool. There's no need to use the pen for everything. In addition preset shapes often are already symmetric.
Preset shapes must generally be converted to paths for easy node editing because in Inkscape they are not Bezier curves. Use Path > Object to Path.
A practical path editing hint: more likely remove nodes than insert them more. The less you have nodes the easier it is to get nice curves.