I guess one of the reports can be closed, but I provided an example with the python template here: https://developer.blender.org/T93430
The explanation of how to reproduce this with the custom node template is also given there:

When creating custom python nodes that have only custom sockets, the node can't be dropped onto an existing link. This is not the case if the node has normal blender sockets, only with custom ones. It also doesn't happen if the node has blender and custom sockets as the blender sockets will be connected and the custom ones ignored.

If I were to throw a wild guess out there why this is happening, I would say that it might have to do with a fix for the float curve node in geometry nodes being connected to the factor input instead of the value input. This was an issue for a while and seems to recently have gotten fixed. I would guess that this somehow looks for compatible sockets and that doesn't consider custom python sockets. I couldn't find the exact commit for this, but it might be a starting point for where to look.

@Joshua Knauber (JoshuaKnauber) @Philipp Oeser (lichtwerk)

I think Joshua figured it out, here is my script for the node, it uses custom float socket.

I can't share the entire script here, but I can email it if you like.

Node UI

class TNODES_ND_clip(bpy.types.Node):
    bl_idname = 'TNODES_ND_clip'
    bl_label = 'Clip'
    bl_icon = 'DRIVER_DISTANCE'
    bl_type = 'TNODES'
    bl_width_default = 200


    def init(self, context):
        self.inputs.new('TNODES_FloatSocket', 'Value')
        self.inputs.new('TNODES_FloatSocket', 'Minimum')
        self.inputs.new('TNODES_FloatSocket', 'Maximum')
        self.outputs.new('TNODES_BasicSocketNoUpdate', 'Value')

        self.inputs["Maximum"].default_value = 1

Custom Float socket

class TNODES_FloatSocket(bpy.types.NodeSocket):
    bl_idname = 'TNODES_FloatSocket'
    bl_label = "Custom Node Socket"

    def prop_update(self, context):
        if hasattr(context, 'node'):
            reset_connections(context.node)

    default_value: FloatProperty(
        description='Custom Height',
        min=0,
        default=0,
        precision=5,
        step=0.1,
        update=prop_update)

Will close this as a duplicate of T93430: Custom node sockets don't get relinked when dropping a node on an existing link

Thanks for the report.