The problem is that the recorder never goes into record mode in your video, and will not pass signal until it does. It needs to be either in record/pause [hold pause down while pressing record, rec button should start blinking] or recording [rec button solid red] to pass signal to the onscreen meters, SD card, and/or the outputs. The hold switch looks to be not engaged, which was the first thing I looked for.
Try a factory reset, then see if you can get it into record/pause or record mode.
Some clarification, but not the core issue-
The SM58 does not need or want phantom but will need more gain before levels are high enough to move the meters, which in that screen mode go down only to -40dB, meaning soft sounds may not ping the meter, but you should see other indications of recording on screen and via a red illuminated record button. AT853 need phantom power before it will produce any output.