How to Select a nbr. per section OR instrument ?

The text that MuseScore puts in that position is the "Instrument Name". Right-click on a blank point in a measure of the score you want to change the name of. If it's a grand staff score (as your example screenshot appears to indicate), right-click on a measure in the tenor clef. From the context menu, click on Staff/Part properties.

Under Part properties, the Long instrument name appears at the beginning of each Section (where the stave is indented). the Short instrument name appears at the beginning of each system, other than that first system of the Section. However, this value applies to the entire score. You can't change it for Section 1, Section 2, and so forth.

Instead, I would recommend putting the number in a System Text field and just having it at the top of the first measure of each Section. However, if you insist on it being at that position, set the Long instrument name and Short instrument name fields to blank and change the Offset values in the text field's Properties to put that System Text field where the Long instrument name normally goes.

Horizontal frames are perfect for this.

In Style > Score, uncheck "Enable indentation on first system"

From the top menu: Add > Frames > Insert horizontal Frame

Right click on the frame: Add > Text

Then format the text as needed in Properties.