I would like to create an overlay for my youtube channel that I can easily put into all my videos without having to set it up again and again.
I know how to add a video track and stick an image in there, but how do I save it as an effect?
The simplest way to make it available across all projects in your current database is to add it to a power bin.
To do this, make sure power bins are visible in the media pool by enabling "Show Power Bins" in the View menu, then drag your picture from the timeline to the power bin. Then, to use it, you can access it like you would any normal clip.
This works well for simple .png images with an alpha channel, or even moving video with an alpha, and it's good way to work with frequently-used brand images, logos, bugs, etc.
But it's not technically a dynamic "effect" and won't show up with Resolve's other effects. If you need more control over the elements in your asset -- say, you want to be able to change the text, for example -- you'll need to save a Fusion macro as a .setting file in the appropriate template location for your system. The paths are different, depending on your operating system, but specific details are available in the Resolve Manual. See the chapter, "Converting Fusion Compositions to Edit Effects," for example.