Gaussian blur isn't available in plain OBS, probably because it is very shader-resource intensive.
You can simulate that blurry background with a small workaround.
Create a source you want as blurry background. Put it into a group. We will attach filters to that group. Not to the source directly to uncouple the filters from the source in case you added the source with the "add existing functionality". So we can have a clear version of a source and a blurry scaled version of the same source as background.
Now add the "Scaling/Aspect ratio" filter to the group two times. Yes, two times.
In the first scaling/aspect ratio filter, set Scaling Filtering to Bilinear and enter 9x8 as resolution. This will create a 9x8 version of your image, which will create our blurry mess if upscaled to the canvas again.
In the second scaling/aspect ratio filter, set Scaling filtering to Bilinear and select 1:1 in the Resolution drop down list. Now you will see a blurry source. Close the filters window.
Right-click the group->Transform->stretch to screen to make it occupy the whole screen. Move the group to the bottom, so it acts as filler for whatever piece of background is left black otherwise.
By adding the scaling filter two times it seems we break some OBS optimization to avoid quality loss at downscaling+upscaling again - but this is exactly what we want, so we can use upscaling from some tiny resolution as "making an image blurry".
