Snapping two topology layers together based on point

In QGIS 3.14.15 with GRASS 7.8.3 I have two layers both with correct topology that function how they should. When using the Network Analysis > Service Area tool, they work as they are supposed to. Trace and Shortest path etc.

However, I would like to connect them to each other.

What it currently looks like:

When running a trace on the RED it should also expand the network to the BLUE as they ‘SHOULD’ be connected at the point layer.

I know this is possible with manually editing the topology and simply dragging it to the point or to each other. This works well, though this network is way to large to do manually and I need an automated tool.

I have used grass v.clean to clean up each layer individually, though when trying to use it to connect the two it changes the network too much as it uses all nodes when using the 'snap' tool in v.clean. The distances between the network layer(s) and the point layer range between .5m and 2.5m

What I want it too look like: (as mentioned it is possible manually)

Is there any ‘black hole’ or something that would just ‘suck’ all points to the point layer? Slight variations in the network are acceptable, such as when I adjust it manually. Just need to do this for a couple million points/lines.