you add your block to the walls tag group.
you can add the json by hand (under resources/data/minecraft/tags/blocks), but as it seems you're using data generators already, forge has a BlockTagsProvider which you can extend and override the method registerTags(). in there you can call the helper method getOrCreateBuilder(), and pass the tag group you want, should be under net.minecraft.tags.BlockTags. with the builder you can call add(), and pass a reference to your block (or blocks).
for the item, you need the parent of the item model to be of the inventory model, not the block model. you're using withExistingParent() and calling the model that you're generating for the block. but that's not the model you want. minecraft should have a model under models/block for the wall_inventory (something like that, I know that for buttons it is models/block/button_inventory).
then you can chain .texture(), and set the "texture" attribute to have the texture of your block.
ps.: this kind of posts really should go under Modder Support, not Support & Bug Reports