1. Get the nearest point on layer airports: use overlay_nearest() with optional argument limit:=1. Do the same for layer harbors. You might also add a max_distance() argument.
2. Combine both nearest points with union()
3. Get the closest point to your input out of these two points using closest_point().

The whole expression to do so:

closest_point( union( overlay_nearest ( 'airports', @geometry, limit:=1, max_distance:=1000 )[0], overlay_nearest ( 'harbors', @geometry, limit:=1, max_distance:=1000 )[0] ), @geometry ) 

Screenshot: yellow points 1 and 2 each have either a closest airport or harbor within max. 1000 m, marked with a black ring, created by the expression above; point 3 does not have within 1000 m any harbor or airport:

1. Get the nearest point on layer airports: use overlay_nearest() with the optional argument limit:=1. Do the same for layer harbors. You might also add a max_distance() argument.
2. Combine both nearest points with union()
3. Get the closest point to your input out of these two points using closest_point().

The whole expression to do so:

closest_point( union( overlay_nearest ( 'airports', @geometry, limit:=1, max_distance:=1000 )[0], overlay_nearest ( 'harbors', @geometry, limit:=1, max_distance:=1000 )[0] ), @geometry ) 

Screenshot: yellow points 1 and 2 each have either the closest airport or harbor within max. 1000 m, marked with a black ring, created by the expression above; point 3 does not have within 1000 m any harbor or airport:

1. Get the nearest point on layer airports: use overlay_nearest() with optional argument limit:=1. Do the same for layer harbors.
2. Combine both nearest points with union()
3. Get the closest point to your input out of these two points using closest_point().

The whole expression to do so:

closest_point( union( overlay_nearest ( 'airports', @geometry, limit:=1 )[0], overlay_nearest ( 'harbors', @geometry, limit:=1 )[0] ), @geometry ) 

1. Get the nearest point on layer airports: use overlay_nearest() with optional argument limit:=1. Do the same for layer harbors. You might also add a max_distance() argument.
2. Combine both nearest points with union()
3. Get the closest point to your input out of these two points using closest_point().

The whole expression to do so:

closest_point( union( overlay_nearest ( 'airports', @geometry, limit:=1,   max_distance:=1000  )[0], overlay_nearest ( 'harbors', @geometry, limit:=1, max_distance:=1000 )[0] ), @geometry ) 

Screenshot: yellow points 1 and 2 each have either a closest airport or harbor within max. 1000 m, marked with a black ring, created by the expression above; point 3 does not have within 1000 m any harbor or airport: