When I smile, the nasolabial folds around my mouth deepen. Should I consult about fillers or a lifting procedure first?

Since turning forty, I have been concerned that the nasolabial folds around my mouth look particularly deep in photos. Even when I apply makeup, foundation settles into the wrinkles, and because the corners of my mouth appear to droop, I have been told several times that I look tired. My cheeks remain the same, so I am confused whether the sagging of the corners of my mouth is due to age or if it is because I have lost body fat.
I learned that the approach to nasolabial folds varies depending on the cause. I am wondering if filling in volume with fillers is the right choice if the lines are formed due to sunken cheeks, or if thread lifting or radiofrequency lifting (Shrink or InMode) is better if the folds are caused by sagging skin and fascia. If both apply, I would like to know the best order to proceed. I am concerned about the foreign body sensation or shifting of fillers, and I am hesitant about thread lifting because there are reviews stating that bruising and swelling last a long time.
I heard that it is essential to check skin thickness and cheek fat levels during a consultation. To achieve a natural improvement tailored to my facial condition, which procedure should I consult first? I would appreciate advice from those with experience.