Short answer:
sudo apt install gvfs at-spi2-core
More detail:
The error messages are due to a few missing D-bus services. Usually, these services would be installed with and started under the Desktop environment (Ubuntu Desktop/Gnome, Xfce4, etc.), but that doesn't happen in WSL. WSL's "desktop" is really Windows itself 1. While it's possible to get a Linux desktop running in WSL2 (see other answers), it's hacky and not needed to answer your particular question.
To fix the warnings, you may have to do a few things. First, the "must have" -- Install the missing services. The services that Emacs is trying to reach, according to the warnings, are:
GIO: The Gnome I/O Framework. This is typically a dependency of applications that utilize GVFS (Gnome Virtual Filesystem), a service which allows end-users to access some virtual filesystems in user-space. For example, the "Trashcan" feature in Ubuntu uses GVFS so that, when you delete a file from a GVFS/GIO application, it gets moved to the Trash instead of immediately removed forever. Apparently, Emacs uses GIO and/or GVFS in some way (although I don't know if it uses the Trash function).
AT-SPI: The Assisted Technology Service Provider Interface. I'll be honest -- I had to look this one up myself. It's an interface for Accessibility features, such as screen readers, braille, eye-trackers, etc. Without some higher level service (such as a screen-reader), it probably won't be used. But that's the same with GIO, honestly -- Typically it's some higher-level functionality (like GVFS) that uses GIO.
So to resolve the error messages:
sudo apt install gvfs at-spi2-core
This will install GVFS (which will include GIO as a dependency) and AT-SPI.
Personally, I'm seeing a few other errors, but I think those are due to my own configuration issues, especially based on your comment. For now, I'm editing the other error messages out of this answer.
Footnotes
1 Technically, it's Weston, running an RDP/Rails shell that uses the Windows Remote Desktop client to view the application on the Windows desktop. However, for most users, the end-result is simply that it looks like the Linux GUI application is running on the Windows desktop.
