The press work ( plates )are not centered.
This uneven pull places stress in the direction the screws are NOT made to have. Any torsion load ( uneven unlevel uncentered can cause that to fail in a very spectacular way.
I have zero experience pressing oil but I have 40 plus years pressing bearings, bushings and axles and that is an unsafe setup on your press.
Please be careful.
Center the load.
If it still pulls left or right find out why.
Setup you press for just enough open space to put you weed in there the more compact the forcing screw the straighter your press. You do not want to jack it 8 inches to contact.
Edit**
I would disassemble that press and check the long spring and rods. The right side looks bent onwards but it can be the angle.
You can also use a plumb bob ( that should be hanging on your press for checking ) to look at it.
A line or string and a 1/2 inch nut, a big washer, something with weight to hold at the top of that right side rod assembly and see if the bottom of the string is still in the middle.