Godot Version
Godot 4.7.dev
Question
Source model and animation

Target model and animation import settings:
Target model and retargeted animation:

Godot 4.7.dev
Source model and animation

Target model and animation import settings:
Target model and retargeted animation:

Was the original model on T-Pose? Did the animations file contains a REST animation in T-Pose? Godot can not retarget well animations and models which were not in T-Pose.
The Rest Pose of source model and target model are both T-pose. When importing the animation file, a REST animation is generated. But it still doesn’t work.
Is this related with Overwrite Axis?
https://docs.godotengine.org/en/latest/tutorials/assets_pipeline/retargeting_3d_skeletons.html
This is the most important option for sharing animations in Godot 4, but be aware that this option can produce horrible results if the original Bone Rest set externally is important. If you want to share animations with keeping the original Bone Rest, consider to use the Realtime Retarget Module.
Here are the target model and the animation file—feel free to give it a try if you’d like.
https://drive.google.com/file/d/1XROSI13oHTZ5GxH7EkJ5RFYP2Wa2Dfnq/view?usp=drive_link
Synty’s animation is based on the first frame pose (A-pose?) and Mixamo animation is based on T-pose. Godot’s SkeletonProfileHumanoid requires T-pose. Godot’s show_rest_only cannot distinguish whether the Rest Pose of animation is A or T Pose, which can be distinguished in Advanced Import window or in Blender.
After retargeting skeleton for animations from Mixamo, can show proper idle pose, whereas Synty’s animations cannot.
Enabling Fix Silhouette in both target model and animation file advanced import approximates to the solution.