The issue:

Auctionator Shopping List search results initiated though Skillet-Classic are missing the first item in the shopping list. When initiating the search through the Auctionator interface, I get the correct result, leading me to suspect Skillet-Classic being the source of the issue. It occurs with a lot of different recipes, and is not just limited to Alchemy.

This occurs using:
Skillet-Classic 1.44-bcc
Auctionator 9.2.11-bcc

How to reproduce A:

1. Open the auction house and a profession window
2. Select a recipe
3. Press the Auctionator button for the recipe
4. The search result is missing the first entry of the shopping list

How to reproduce B:

1. Open the auction house and a profession window
2. Queue up some crafts
3. Open the shopping list
4. Press the Auctionator button on the Shopping List window
5. The search result is missing the first entry of the shopping list

Example:

Shopping List search result, initiated using the Auctionator button on the Skillet: Shopping List window. Notice the missing Felweed in the result.

The same shopping list, this time searched using the Search All button in the Auctionator UI. This time the Felweed appears as expected.

debug-logs.zip
Two logs here, one for each of the ways I listed to reproduce.

Here's an updated ...\Addons\Skillet-Classic\Plugins\Auctionator.lua:

Auctionator.zip

It adds a debug for reagents skipped because they are sold by vendors and fixes a bug when using the Auctionator button in Enchanting recipes.

Of course, I forgot one essential command, "/skillet tabledump on".

My attempts to reproduce both cases are failing and the two cases you provided debug logs for I would need screenshots that show the error.

I have queued 1 Fire Oil and 1 Blackmouth Oil. The three screenshots show the results of clicking the Auctionator button in the detail frame for each of the selected recipes and the results of clicking the Auctionator button in the shopping list. You can also see the debug output in the chat frame.

Screenshots.zip

My alchemist is only level 22 with a skill of 168. If you can generate cases which fail using recipes in that range it would help.
I do have a max level tailor who also has max level cooking and first aid. I have a leatherworker that is level 45 with 281 leatherworking and a level 35 enchanter with enchanting at 275.

I'm working on adding more debugging to the Auctionator plugin (which contains the search function). I'll attach that when its done.

Log and screen dumps with the new version of the plugin along with tabledump on
log + screen dumps.zip

For the recipe search, the first item in the list passed to Auctionator is the item itself. You would need to click Search All in the AH frame to show that some exist but aren't being shown. Just out of curiosity, what happens if you make one of these items and put it up for sale? There is also an Auctionator option to show items with zero results.

For the shopping list search, two items are vendor bought (Hot Spices and Mild Spices) and the remaining two items are passed to the Auctionator API and are seen on the left in the AH frame. Your previous two recipe searches show that both items have AH entries and you are absolutely correct, only one shows in the search results on the right of the AH frame.

On my server, the exact same cooking recipes queued, the exact same shopping list, (the exact same debug output) but the search results shows both items in the search results.

I believe Skillet-Classic is doing the right thing but Auctionator is screwing up. At some time in the past, there was a "fan-fixed" version of Auctionator. Do you still have that one installed? If so, uninstall it. Just for my sanity, please delete and reinstall Auctionator-bcc 9.2.11.

I can't create a character on your server. Can you create one on any US servers? I have toons on Azuresong and Whitemane. I'm grasping at straws looking for a common denominator.

I have pushed a slightly newer Auctionator.lua plus another small change into Skillet-Classic-1.45-alpha1.

I did previously have the fan-fix version of Auctionator installed, however I've been using the new version of Auctionator for quite a while now, while the issue only appeared recently. I didn't notice any difference with the 1.45 alpha.
After doing a clean reinstall of WoW, I am no longer able to reproduce the problem. I guess the Auctionator fan-fix could have created a conflict with the official release somehow.

I greatly appreciate the effort you have put into this issue, and the addon in general. It makes crafting a breeze! :-)

I'm trying to reproduce this. In the mean time, you could capture some debug output for me.

Type "/skillet debugshow on" and "/skillet debuglevel 2" so Skillet-Classic will output to chat and to your character specific saved variables file Skillet-Classic.lua the contents of the tables it sends to Auctionator (as well as a lot of other stuff).
Logout (or "/reload") after demonstrating the issue and upload the character specific saved variables file here. You will need to either rename it from .lua to .txt or zip it as GitHub doesn't like .lua uploads.

Use "/skillet cleardebuglog" to clear the log between experiments and "/skillet debugshow off" to turn off logging to chat (logging to the saved variables file will remain on, "/skillet debugoff" will turn everything off). The logging to the saved variables file doesn't use a lot of resources and only keeps the most recent data so you can leave it on.