Craft filter in the inventory
 

Does anybody know an Addon which allows to filter inventory (Armor and Weapon) by craft areas (Clothes, Woodworking, Blacksmith, etc.)?

Advanced Filters does this already.
But: The inventory cannot be split into exactly these crafting types as it comes prefiltered with standard categories (weapons, armor are strictly divided e.g. and cannot be combined on 1 filter to show "Smithing"). Same for Shields and staffs which are armor and weapons -> Not possible to combine them.
AF is providing subfilters for the given top category filters + plugins in the dropdown boxes which help you to filter them even more.
But that's all you will get as an addon ecept someone is totally rewriting the inventory...

A helper could be that AF is filtering the crafting inventories at the crafting stations as well,
and in addition FCO CraftFilter provides ways to switch between "Show bank", "Show only inventory", "Show both", "Only show craftbag" (at refine panel).

Another addon to help would be Inventory Insight as it also provides similar filters but shows ALL your toons/characters + bank + guild bank inventories in one UI.

Oh it's Mr. Baertram in propria persona! :) I'm glad to see you :)

I've tested Advanced Filter. It's very comfortable but I didn't find the way to filter out "Clothing" or "Woodworking" items from my list.

Did I understand you right that it's basically NOT possible to split items into Crafting areas in the inventory?

Yes, correct. It's not possible without breaking the total inventory and having to re-write Zos code a lot!
I bet noone is going to try this except in an own UI (like Inventory Insight does), not using the vanilla UI inventory.

Here is what to select for the craftings with vanilla UI:
Clothing: Armor->Light + Medium
Woodworking: Armor->Shields, Weapons->Staffs (Deconstruction, Healing) + Bows
Smithing: Armor->Heavy, Weapons->1hd + 2hd
Jewelry: Jewelry

As you can see this is not possible to show on 1 tab so you need to select them after another.

AutoCategory can separate out categories - you just have to create the categories and add them to the bag view where you want them applied.

For instance a clothing category could be defined as
and added to the backpack to create a clothing section with all the items that are armor and either light or medium.