How to get the BBOX of selected features in QGIS using the UI?

Not sure this is what you want to see...anyway,

(1) Open attribute table and add a new text field (length ~ 160) with an expression: geom_to_wkt(bounds($geometry))

(2) Click on Identify Features icon

If you are after the bounding box coordinates you could use the following expression when creating a new text field via the QGIS Field Calculator:

array_to_string(array(
    x_min($geometry),
    y_min($geometry),
    x_max($geometry),
    y_max($geometry)
))

This will produce a text value of the minimum x, minimum y, maximum x and maximum y coordinates of a given feature, comma separated.

Out of the box feature to this is to open python console, and write one simple line:

iface.activeLayer().boundingBoxOfSelected()

Too bad if you do not want to use python console. Feel free to open feature request for a new tool. I think some optional selection information tab with count of selected features and few more stats would be nice. I am not aware of anything existing, this might be a long wait.

In summary, you want QGIS to show you in its interface the bounding box coordinates of one or more selected geometries, without using Python.

Is this possible? Yes, with the magic of expressions, I show you.

@Gnafu I think, that for your case the ideal is to configure the Map Tip of the layer.

The first thing is to clarify that the bbox is defined by four extreme coordinates, xmin,xmax,ymin,ymax. These coordinates define the minimum rectangle of a polygon or a group of geometries, and are the ones that we are going to show.

Procedure:

1.- Open the polygon layer properties dialog box. Then go to the display tab. 2.- click on the button with the eplison symbol (capital e, highlighted with a red box in the image), located at the top. Write the following expression

'Xmax y Xmin: '+to_string(round(x_max(collect($geometry, is_selected())),2)) +  ','  + to_string(round(x_min(collect($geometry, is_selected())),2)) +  'n'  + 
'Ymax y Ymin: '+to_string(round(y_max(collect($geometry, is_selected())),2)) +  ','  + to_string(round(y_min(collect($geometry, is_selected())),2)) 

Then, next - apply - Ok.

To test it, activate the Map Tip button

Now, select a polygon and place the cursor on it. You will see its extreme coordinates. Then, add to the selection other polygons, you will see how the coordinates change