Two screens means two protectors, and they aren’t interchangeable. The Galaxy Z Fold 8 Ultra has a 6.5-inch cover screen on the outside and an 8-inch folding screen inside. Each one needs a different kind of protection, starting with the cover screen, since it's more likely to receive more impact.
Samsung uses Gorilla Glass Ceramic 3 there, which handles drops quite well, and a regular tempered glass protector will do just fine. The inner screen is an 8-inch panel uses Ultra Thin Glass that bends, so any protector you put on it has to bend with it and rigid tempered glass won't do.
You need a flexible TPU or PET film, which the company's earlier Folds shipped. They had a preapplied film, and if your phone came with one, keep it on until it starts peeling. But if it has served its purpose, here are great replacement options.
Spigen GlasTR EZ FIT cover screen glass
$20.99
ZAGG Glass Elite cover screen protector
$34.99
TAURI 2-pack cover glass with tray
$9.98
apiker inner film and cover glass combo
$22.99
WSKEN zero bubble dual-screen kit
$35.99
TOCOL auto-align cover glass
$8.99
Get the install right
For your phone's inner screen, fully unfold the Z Fold8 and put it on a flat surface before you start, so the film goes on without tension at the crease. Wait some hours before folding it closed, otherwise the film lifts at the hinge.
If you use a case, check that your protector is labeled case friendly. Edge-to-edge glass on the cover screen can get pushed up by a raised case lip and the corners will peel.