Hi! A few things first. First, a schematic and PCB review usually takes multiple hours in person, even when data sheets and the schematics have been sent ahead of time. If I may ask, what program are you using to create this? I've had a lot of luck with KiCAD (free and open source) for my personal projects, though I've used Altium and Eagle in my professional life (Eagle less so).
@Deva_Rishi had a really good point - get everything working with a breadboard or by soldering wires together first, before ordering a PCB. It will help you solve a lot of the problems you'll run into just trying to get the thing to work. Also, nobody gets it right in the first revision (even the second, or the third...), even professionals. There are always a few small things that you find when you order your boards that are wrong.
Okay, so, let's get into it. The first thing that I notice right off the bat is that your BMP 388 is not going to communicate. There are two main digital communication protocols - I2C ("i squared c") and SPI. They are very different. The GY-521 uses I2C, and the BMP 388 uses SPI. This means that you cannot hook them up to the same signals. You'll need independent traces going to each, as they're different protocols.
To use SPI, it doesn't have an address like I2C, it has a CS (or Chip Select) pin that you have to drive low (to ground) in order for it to listen to the commands on the bus. There are usually libraries that do that for your specific device, so you might look into if anyone has written a BMP 388 library.
Again, to @Deva_Rishi 's point, there are certain pins that you cannot use for General Purpose I/O (GPIO) on the ESP32. I use ESP32's all the time, and this drives me crazy. There are also default pins for I2C and SPI that will make your life a lot easier when coding. Just look up your version of the ESP32 and "pinout" at the end, and your favorite search engine should show you the default pins. I'd highly recommend using those.
If you haven't already, I'd look through the device's datasheets. They usually tell you how to wire them up (some even include a "best practice" board layout that I'd recommend you try to accommodate).
To be completely honest, I haven't studied your schematic or board layout too much. However, on your board layout, on the bottom layer (I assume - it's the blue layer), on the right side, about halfway up the board, there's a (what I assume to be 5V) trace that does a little wiggle around a via. Try to avoid those as the board manufacturer will have difficulty getting that right. Instead, drag that part of the trace (where it's going up the board) to the left a little bit to get rid of that wiggle and make is straight. The more straight lines, the better.