Can you export a png file to have the multiply blend setting?

The blending mode can’t be carried with an image because it’s always applied by the application using the image. As soon as the image leaves Illustrator, Illustrator can no longer control the blend mode. if you want to apply Multiply in Canva or Google Slides, those applications would have to be able to apply Multiply.

It looks like it is possible if you were using it as a graphic on a web page you control, because blending modes are supported in CSS:

Basics of CSS Blend Modes

A workaround for this problem is to “premultiply” the background: If you know it will be shown over a specific color like the green in your example, you export not just the graphic, but the graphic over the same green background so that it will match up in the second application. But this can be tricky because it only works with the one color it was premultiplied with, and if the color is off in either application it will visibly not match..

I know it's likely impossible

By @Nick Alonzo

Good instinct.