After inspecting your blend file I've come to the following conclusion.
The cause of unwanted deformations is the presence of Stretch To Constraint on some of your Deform bones. If you use Blender 4.0 they will be located in Layer 30.
Unfortunately this constraint has an option to maintain the objects volume when stretched which unfortunately cannot be translated perfectly to just bone scale keys.
However it seems the exporter attempts to compensate for that option which causes undesirable result.
With this Constraint available there is no perfect solution but the best you can do is to set the Maintain Volume to None to all deforming bones
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/KuysB.png)
Deforming bones in Layer 30, set Maintain Volume to None to all Stretch To constraints in that layer.
Your FBX export settings are fine and with the above recommendation you will get the following import back in Blender:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/jFFtL.png)
Unfortunately you can't get the exact result back due to the nature of the Stretch To constraint, which is now missing in the FBX import.
Alternatively, You can try correcting the animations of the character with disabled / removed / Stretch To constraints from the deform bones.