Bug Description
The vanilla lantern placed on the side of a wall becomes a wall lantern from the torch slabs mod, this has no correct tool and when mined does not drop the lantern
Steps to reproduce
Place lantern on wall
break it
Expected behaviour
Have proper tool (pickaxe) and drop the lantern

I encountered the same problem with the soul lantern.

Same issue still happening on 1.19.2

You can fix this by adding the lantern(s) to the minecraft:mineable/pickaxe tag.
You can do this by making a datapack or using KubeJS for example, like I did, with following code in a server script:

ServerEvents.tags('block', (event) => {
    // This fixes lanterns converted by Torch Slab Mod not being mineable
    // + it fixes the lanterns not being dropped as items when mined
    event.add('minecraft:mineable/pickaxe', [/^torchslabmod:.*lantern$/]);
});