Sensor fusion can help the precision even in orientation in the plane perpendicular to gravity
I meant, what is the claimed application for this specific fusion algorithm? Manufacturer of the chip (and the algorithm) should be saying something about what it can do and to what accuracy - and also have application notes how to achieve this accuracy (e.g. PCB layout).
Apologies, I was apparently particularly dense yesterday.

Yes, fully agreed.
After looking at the 28-pin LGA footprint, I'm pretty sure OP is talking about Bosch BNO055 9DoF sensor;
PDF datasheet,
documentation. Or possibly a clone. It is not a particularly good or precise 9DoF sensor, though.
Sensor fusion isn't difficult to implement yourself, though. You can find many open source ones for the 9DoF MPU9250, for example. I do believe some are so disappointed at the BNO055 built-in one that they prefer to use it as a dumb 9DoF IMU and run their own Madgwick sensor fusion algorithm on a suitable microcontroller.
Whatever you do, learn to use versors/unit quaternions/bivectors –– four-component \$(q, i, j, k)\$ objects –– for the orientation and describing rotations in general.
Euler and Tait-Bryan angles will lead you astray, because they are actually an ordered set of rotations around specific axes, with at least the third one dependent on the first two and thus leading to gimbal lock, and nobody agreeing to exactly what axes are to be rotated in which order, leading to many different variants used under the same name, leading to surprising issues when part of your implementation uses a different one by accident.
Perhaps I should write a post to the Beginners section to describe the operations needed. Euler/Tait-Bryan angles users too often fall into its traps, thinking they're easier than the versor/quaternion/bivector approach, but it's just not true! And using 3×3 matrices (or two unit vectors perpendicular to each other, the third being the cross product of the first two) is just too cumbersome.