QGIS expression with overlay-fuction: filter-condition based on comparison of attributes from two layers

I tested some configurations, tried to understand how it works. So ! I figure it out.

The scope of the filter parameter in the expression function of overlay_nearest is purely the layer set in the layer argument, as if you put this expression in the layer select by expression.

To achieve your goal, I came up with another solution. Instead of select the nearest $geometry of the other layer, I selected the nearest $currentfeature. And in the end, instead of building a line directly, I put an if condition to return a NULL geometry if the nearest layer_2 feature id2 equals the current id1.

collect_geometries(
    array_foreach(
        overlay_nearest(
            'layer_2',
            $currentfeature,
            limit:=1
        ),
        if(
            condition:=attribute(@element, 'id2') = "id1",
            result_when_true:=NULL,
            result_when_false:=make_line(geometry(@element), $geometry)
        )
    )
)

With the QGIS expression above, if you increase the overlay_nearest limit, say 2 instead of 1, if one of the collected geometries is NULL because it meets the condition, it nullifies all the geometries and it's not what we want.

Just replace in this case the NULL condition result with a zero lenght line :

collect_geometries(
    array_foreach(
        overlay_nearest(
            'layer_2',
            $currentfeature,
            limit:=2 -- update here
        ),
        if(
            condition:=attribute(@element, 'id2') = "id1",
            result_when_true:=make_line($geometry, $geometry), -- update here
            result_when_false:=make_line(geometry(@element), $geometry)
        )
    )
)

Hey ! Yes it works but when layer_1.id1 = layer_2.id2 I got only one line for this point ...

Okay ... I heard you, you are right, GIS is a demanding discipline so I'm reviewing my copy !

To achieve this, I defined a variable, placed on top for easy access, lines_per_point. You can set the number of lines per point, here 2.

With the comment of @MrXsquared, I used array_filter instead an if condition in the array_for_each, it drops all NULL values.

But ! I increased by 1 the overlay_nearest limit of features returned (I considered that layer_2 identifiants are unique, so filter can drop for one layer_1 point only one line maximum (when layer_1.id1 = layer_2.id2)).

Ok, it returns arrays of lenght 2 or 3. Here I used array_slice to get only the two first features (beware, the slice doesn't work as a Python list, it includes the 2 bounds), so [0, 1], so [0, lines_per_point - 1].

We have now an array of length 2 with layer_2 features. So, I applied an array_foreach to create the line with make_line(geometry(@element), $geometry).

(Obviously, you'll get different number of lines for each layer_1 points if the lines per point equals the number of features of layer_2)

The QGIS expression below :

with_variable('lines_per_point', 2,  -- adjust here
collect_geometries(
    array_foreach(
        array_slice(
            array_filter(
                overlay_nearest(
                    'layer_2',
                    $currentfeature,
                    limit:=@lines_per_point + 1
                ),
                attribute(@element,'id2') <> "id1"
            ),
            0, @lines_per_point - 1
        ),
        make_line(geometry(@element), $geometry)
    )
))