German Brewing

Aren't wooden spoons often coated with mineral oil as well?

Honestly, nobody knows if it makes a difference, but the most likely answer is that it does not. Nonetheless, if one is to choose, at some point in time one may need a spoon in the cold side, and sanitizing a wooden spoon may not be as easy as sanitizing a stainless one.

As a side comment, and just speaking about me, I consider myself a good brewer but I will never achieve the Nirvana of brewing and tasting at a the level that would be able to catch a difference between a wooden and stainless spoon should there be one
There are many parts of my process that I need to fine-tune before I get to spoons. Among them:
- Specialized mashing for weissbier (maltase rest? ferulic rest? protein rest?) - what are the effects of LOX during these rests?
- Specialized mashing for dark beers (protein rest?)
just to name a few...

Have not opened the barrels so I have no direct evidence to the contrary
When I toured Paulaner in 2011, I understood that the kegs were completely made of wood. See attached file in English for add info.
I also know that a few brewery-restaurants offer Helles von Holzfass regularly. I lived by Viktualienmarkt so I went by Der Schorr regularly and they often advertised Holzfass Helles; knowing the Germans, I find difficult to believe that the advertised Holzfass was stainless inside (they take these things seriously --see Reinheitsgebot-- .
Nonetheless, it is quite possible the majority of the kegs that appear to be wooden, are stainless inside. Honestly, never bothered to check.
Cheers,