Should I find a specialist for specific procedures or combine them?

While you can certainly do eyelid and facelift surgery separately, it's always better to do things together if possible. A facial plastic specialist with a lot of experience will do this combination procedure often and should be able give a great result.

As an Oculofacial plastic surgeon, a few of the procedures I perform are advanced upper and lower eyelid blepharoplasty techniques, eyelid reconstruction, revision eyelid surgery, deep-plane face and neck lifts, and revision deep-plane face and neck lifts.

There are variations in surgeon’s trainings, skills, experience, and ability. The decision is up to you as the whether you want to split them up or do them together but you need to be comfortable with your decision.

This is a great question because not all Oculoplastic surgeons are "Oculofacial" plastic surgeons.
Some limit their practice to eyelids and eyebrows, while some of us do the full range of face and neck rejuvenation.
Review their website to see what types of procedures they offer, and more importantly review their before and after photos and make sure that the results are in line with what you are looking for. I also recommend that they are ASOPRS-trained. The American Society of Ophthalmic Plastic and Reconstructive Surgery sets the standards of training for Oculoplastics and Oculofacial Plastic Surgeons.
Virtual consultations are available (see link below)

if you wanna perform both procedures simultaneously under one anesthesia with one recovery period, then consider a board-certified facial plastic surgeon with extensive experience, performing both eyelid surgery and face /neck lifts. Study your perspective surgeon’s before and after photo gallery, specifically for eyelids and facelift procedures. It should be extensive with lots of natural looking results that you like.