Selecting lines intersecting lines on two points in QGIS 3.14

I have two shapes of lines: one A with exploded red lines, the other B with closed black lines.

In a virtual layer I want to select the yellow ones (A) i.e. those having only 2 points in common with B.

I try to find a way to count the number of intersections between 2 lines without success.

Or maybe there is a better way to do it.

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@JGH There is something weird when I work with my data. I can’t get the result you show on your screenshot. When I run the query to get the same result as you:

SELECT poly.*
FROM input1 as poly, input2 AS ouverture 
WHERE st_intersects(poly.geometry, ouverture.geometry)
AND st_dimension(st_intersection(poly.geometry, ouverture.geometry)) = 0

Then the result is the red lines :

The green polygons (poly) have only 4 nodes and topology is correct with black lines. It runs from a model so green polygon file converted to lines is not visible.
The strangest are the two red lines at the bottom which are the opposite of the expected result.

@Taras : result is empty.

EDIT : sample of data
shp and comments inside.

SELECT tg.*
FROM target_layer AS tg, closes_line_layer AS cl 
WHERE st_intersects(tg.geometry, cl.geometry)
AND ST_Dimension(st_intersection(tg.geometry, cl.geometry)) = 0

SELECT r.*
FROM "red_lines" AS r, "black_lines" AS b 
WHERE st_within(start_point(r.geometry), b.geometry)
AND st_within(end_point(r.geometry), b.geometry)
AND st_length(st_intersection(r.geometry, b.geometry)) = 0