Just catching up on this thread and man, I totally feel your pain. Chicago architecture is beautiful but it is a total nightmare to shoot if you are stuck with a standard zoom lens. Honestly, don't overthink the technical specs too much right now, you just need something wider. If you want something that feels sturdy and works really well for those big city buildings, take a look at the Samyang 12mm f/2.0 NCS CS. It is manual focus, which sounds intimidating, but for landscapes and buildings, it is actually super easy to use because you can just set it to infinity and everything stays sharp. It is way cheaper than the Fuji glass and gives you that super wide look you are clearly missing. Another solid pick if you really want that autofocus convenience is the Sigma 16mm f/1.4 DC DN Contemporary. It is a little bigger than the pancake lenses, but the image quality is absolutely stunning and it handles low light like a champ. Either of those will fit your budget just fine and honestly make your shots look way more professional than what you are dealing with now. Just remember to keep your camera level when shooting tall buildings so they dont look like they are falling over!

Adding my two cents here since I prefer to stick with what is reliable when you are traveling. When you are just starting, third-party stuff can be a bit of a gamble with quality control, so I usually lean toward native glass or established brands. Since you are worried about getting it right for your trip, check out the Fujifilm XC 15-45mm f/3.5-5.6 OIS PZ. It is extremely affordable and gives you that zoom flexibility, which is nice because you aren't stuck at one distance. It might not be the fastest lens out there, but the stabilization is solid for handheld shots of buildings. If you really want to step up the image quality and dont mind spending a bit more, look at the Sigma 16mm f/1.4 DC DN Contemporary. It is a bit bigger than the Fuji options, but the build quality is fantastic and it handles low light way better. You get very sharp results which makes editing later much easier. Just remember that with wider lenses, keep your camera level. If you tilt it up too much, the buildings will start to look like they are falling backward. It is just basic geometry, but it makes a huge difference in your final shot. Either of these should fit your budget and save you from the stress of dealing with manual focus or weird adapters.

TL;DR: Grab the Fujifilm XF 16mm f/2.8 R WR and you will be golden! Seriously, I remember being just as frustrated when I started shooting Chicago architecture, but this lens changed everything for me. It is super compact, which is perfect for travel, and the glass is just fantastic for the price! You wont have to worry about weird distortion, and the weather sealing is a total lifesaver if you hit some rain in Cali. I honestly love it so much because it feels sturdy and reliable without being a massive heavy brick in your bag. Just pop it on your X-S20 and you are gonna see a huge difference in those landscape shots immediately! Good luck with the trip!

Re: "Just catching up on this thread and man, I totally feel your pain." Honestly, I was in your shoes last summer trying to capture these massive cathedrals in Europe and kept cropping off the tops. I spent my savings on gear initially and realized later that simply learning how to frame the shot mattered way more than the brand on the lens. Just practice walking back a bit more and keep your camera level to avoid that weird distortion!