To get an array with the length of the border the current polygon shares with all bordering polygons, use this expression:

Convert it to a string with array_to_string(), add the $id to identify to polygons etc.

A polygon layer with an expression-generated label, based on the expression from above, that generates a text-string list of length with all neighboring polygons (see below for the expression used here:

• The expression used to generate the red line in the screenshot, using Geometry generator:

if ($id = 1, intersection ( $geometry, overlay_touches (@layer, $geometry)[0]),'')

• The expression used to generate the label in the screenshot - can be used without changes on any polygon layer:

'Length border of polygon '  || 
$id || ' with: '  ||  '\n'  ||  
array_to_string (
    array_foreach (
        overlay_touches (@layer, $id),
        '   - polygon'  || 
        @element || ': ' || 
        round (
            length (
                intersection (
                    $geometry, 
                    geometry (
                        get_feature_by_id (
                            @layer, 
                            @element
                        )
                    )
                )
            ), 
            3
        ) 
    )
)

Calculate the length of the border the current polygon shares with all bordering polygons, use this expression that creates an array:

Convert it to a string with array_to_string(), add the $id to identify the polygons and add other modifications (see below).

A polygon layer with an expression-generated label, based on the expression from above, that generates a text-string list of length with all neighboring polygons (see below for the exact expression used here):

• The expression used to generate the red line in the screenshot, using Geometry generator:

  if ($id = 1, intersection ( $geometry, overlay_touches (@layer, $geometry)[0]),'')
  

• To generate the length of the common boundary line of polygons b and c, stored in the field named name, use this expression (change layer name and value in lines 2 and 6):

  if (
      name = 'b', 
      length(
          intersection ( 
              $geometry, 
              geometry (get_feature (@layer, 'name', 'c'))
          )
      ),
      ''
  )
  

• The expression used to generate the label in the screenshot - can be used without changes on any polygon layer:

   'Length border of polygon '  || 
   $id || ' with: '  ||  '\n'  ||  
   array_to_string (
       array_foreach (
           overlay_touches (@layer, $id),
           '   - polygon'  || 
           @element || ': ' || 
           round (
               length (
                   intersection (
                       $geometry, 
                       geometry (
                           get_feature_by_id (
                               @layer, 
                               @element
                           )
                       )
                   )
               ), 
               3
           ) 
       )
   )
  

To get an array with the length of the border the current polygon shares with all bordering polygons, use this expression:

    array_foreach (
        overlay_touches (@layer, $geometry),
        length (intersection ($geometry, @element))  
    )

Convert it to a string with array_to_string(), add the $id to identify to polygons etc.

To get an array with the length of the border the current polygon shares with all bordering polygons, use this expression:

    array_foreach (
        overlay_touches (@layer, $geometry),
        length (intersection ($geometry, @element))  
    )

Convert it to a string with array_to_string(), add the $id to identify to polygons etc.

A polygon layer with an expression-generated label, based on the expression from above, that generates a text-string list of length with all neighboring polygons (see below for the expression used here:

• The expression used to generate the red line in the screenshot, using Geometry generator:

if ($id = 1, intersection ( $geometry, overlay_touches (@layer, $geometry)[0]),'')

• The expression used to generate the label in the screenshot - can be used without changes on any polygon layer:

'Length border of polygon '  || 
$id || ' with: '  ||  '\n'  ||  
array_to_string (
    array_foreach (
        overlay_touches (@layer, $id),
        '   - polygon'  || 
        @element || ': ' || 
        round (
            length (
                intersection (
                    $geometry, 
                    geometry (
                        get_feature_by_id (
                            @layer, 
                            @element
                        )
                    )
                )
            ), 
            3
        ) 
    )
)