Exporting raster from QGIS to use it in other programs

I am having a hard time trying to set a raster in a way that I can use it in AutoCAD map, for example. So these are the steps that I am doing:

Below is the image from the google satellite with the vectors of the lanes (in UTM Zone 23S, as is the project)

I then exported the map as image, and as you can see in the print below, when I put the output image it in QGIS, it landed in the right place.

Well, with the little I know about projections, I thought I had successfully exported the image so I could use it in AutoCAD map. Then I just went and exported the vectors as dxf, in UTM zone 23s as well, but when I tried to import both the raster and new dxf they weren’t in the same place at all!

To better explain all my steps, I’m inserting here what I’m doing when importing the data to AutoCAD map.

First I’m converting the vector to dxf in QGIS in Sirgas 2000 UTM 23S

Then I’m opening the dxf file in AutoCAD map and assigning the coordinate system (Sirgas 2000 UTM 23S)

And lastly I’m importing the raster created when I imported as image in QGIS

Here the result of the journey, the vector in a place and the raster far away from it

Could someone help me to understand what did I do wrong and how could I achieve the results that I’m seeking?