System Information
Operating system: Windows 10

Blender Version
Broken: 3.2.0
Worked: 3.1.2

Short description of error
Set desired vertex color channel by click on camera icon to bake doesnt work. Baking are always happened for channel which was created first. I.e. it doesnt matter how you name you channels, it doesnt matter which of them are marked as active for baking by camera icon on the list. Baking will always write info into channel which was created first.
If you press on adding button and have Color, Color.001, Color.002,... baking will happen for Color because it was the first one created.

Exact steps for others to reproduce the error
Create at least 2 vertex color channels. Try to select any vertex color channel by click on camera icon, but not the first one which was created, top make that channel active for bake. Bake something. Baking will happen for first created channel.