I agree that keeping it simple is the way to go. Honestly, I've been happy with the ULBTER X-E4 Screen Protector 3-Pack, no complaints here and it works well. For the strap, the Peak Design Cuff Camera Wrist Strap is super handy because it wont get tangled in your bag. If you're worried about scratches, a Tenba Tools Protective Wrap 12-inch is a solid alternative to a bulky case.

Building on the earlier suggestion, I totally get the anxiety about scratching a new camera! Tokyo is going to be amazing but those crowds at Shibuya are no joke. Since you are on a tight budget, I have two favorites that keep everything safe. First, check out the JJC OC-F1BK Neoprene Camera Pouch. I love it because it is thick and squishy, way better than just a thin cloth. It fits the X-E4 with that pancake lens like a glove. The pros are it is super cheap and actually covers the dials on top. The only real con is you have to take it off to shoot, so just dont drop it while its naked... Second is the SmallRig L-Shape Grip for FUJIFILM X-E4 3231. This is fantastic because it adds a bit of metal around the bottom and side. If you bump into a wall, the metal takes the hit, not your expensive camera body! Plus it makes the tiny camera way easier to hold so it wont slip out of your hands. Pros are the extra protection and better handling, tho the con is it adds a tiny bit of weight. Both of these together are well under your $60 limit and honestly they are better than any fancy leather case for safety. Have the best trip ever!

Just seeing this now and man, Tokyo is gonna be a blast. Since youre on a budget and leaving so soon, definitely skip those fancy leather half cases. They look stylish but basically do nothing to protect the lens or the top dials if you bump into a pole in the Shibuya crossing. Honestly, if you want it to fit in a jacket pocket, just get a simple neoprene sleeve. I use the MegaGear Ultra Light Neoprene Camera Case for my XE4 and its perfect because its basically just a wetsuit for your camera. It protects it from scratches while its in your bag or pocket but you can rip it off in a second when you see a cool shot. The X-E4 is super slippery tho so be careful. I would suggest grabbing a thumb grip even if you think it might make it too bulky. Something like the Haoge THB-X4B Thumb Up Rest for Fujifilm X-E4 makes a huge difference in how the camera feels in your hand. It actually makes it feel way more secure so you wont drop it as easily. It adds like a tiny bit of height but it shouldnt mess with a soft case too much. For the strap, look at a simple paracord one like the Vancity 604 Paracord Camera Wrist Strap. Its cheap, indestructible, and wont get tangled like those flat nylon ones that come in the box. Just make sure to double check your shipping times so it actually hits your door before the flight. Dont overthink it too much or youll drive yourself crazy before you even get on the plane... just focus on the food once you get there.