3D carving and 2D cutting goes off path

This happens only with load on machine.

Troubleshooting :
Increased current on the driver (DRV8824) of x axis
re adjusted v wheels
changed all 3 belts, and tensioned as described

My machine settings :

I can engrave on metal sheet with spring loaded diamond engraver (Spindle off) without issues.

I’ll be thankful to anyone who suggest me the best tricks to resolve this issue

Just a thought but are you using a ramp cut to start?

So either slipping pulley for the belt, or you are taking to big a bite and the tool is deflecting (either by actually bending or causing the motor to skip steps). Easel essentially slots for profiling so it can put a lot of pressure on the tool compared to an adaptive tool path.

What is the max depth of that 3D carve?
You may want to consider a roughing cut first.

This happens on roughing cut also
Even on 2d cutting, it does the same.
It goes off only on X axis
cutting depth 1.7mm per pass, 1/32" bit