What type of surgery would be recommended to get "fox eyes"? Lateral vs Endoscopic brow lift? (Photo)

A brow lift (Endoscopic or temporal) will certainly raise the brows like Bella Hadid's, however the eyelid shape is not going to be changed predictably. You will need canthopexy/canthoplasty, likely combined with lower lid retraction repair for a permanent, predictable result.
It would be a good idea to post a photo to see if you are even a good candidate for above procedures.

This is an increasingly popular request from patients, the “fox eyes” or “cat eyes” look. In the upper face, the only structures that can be manipulated are the lateral or full brow, the upper eyelids, and the lower eyelids. The brow can be treated both open or endoscopically. It depends on your surgeon’s experience and preference. Seek out an experienced surgeon and have a detailed discussion in front of a mirror on the best method to achieve your goal. I wish you the best!

The specific procedures are based on each individual anatomy and desired with understanding of risks and limitations of surgery. See an expert.

Depending on your present brow position this may be accomplished with either a lateral brow lift or a full endoscopic brow lift. If you already have good brow height and just want a small lateral lift then a lateral brow lift would be the best option. If you have drooping or laxity of the entire brow then a full, endoscopic brow lift would be the best choice. The complete endoscopic brow lift is the best operation as you have control of the height, shape and contour of the entire brow with complete release and fixation of the brow. That said, if the overall brow position is good then a lateral lift, which is less powerful and more subtle, can still do the job. Consulting with a surgeon experienced in these brow lifting techniques would be a great way to get more information on these procedures.

Endoscopic approach is probably the best avenue to provide a satisfactory cosmetic result with minimal scars and no sensory or hair loss. Consultation with a board-certified plastic surgeon that performs a fair number of endoscopic procedures can probably give you an exact description and illustration or what you can expect from this procedure.