Those examples are not wood, they are probably cast stone.

https://www.houzz.com/pvp/newport-cast-stone-fireplace-mantel-pearl-prpv-pv~85916038?m_refid=PLA_HZ_85916038

https://www.etsy.com/listing/245057062/wasatch-stone-fireplace-mantel?gpla=1&gao=1&&utm_source=google&utm_medium=cpc&utm_campaign=shopping_us_ps-a-home_and_living-home_decor-other&utm_custom1=k_Cj0KCQiA4L2BBhCvARIsAO0SBdZshG1nB8eBlbnWhr2QIzZ3Sp0oKE-NoJMy66Q2FLVpvXUCmUIKm8aAoZREALw_wcB_k_&utm_content=go_920092452_49711316081_218668961727_aud-952490157790:pla-303663660129_c__245057062_141913464&utm_custom2=920092452&gclid=Cj0KCQiA4L2BBhCvARIsAO0SBdZshG1nB8eBlbnWhr2QIzZ3Sp0oKE_-NoJMy66Q2FLVpvXUCmUIKm8aAoZREALw_wcB

I know there are different codes for this, but I am struggling to find a clear answer.

If you just search for fireplace clearances, it is very confusing with all kinds of different information. Here's how it works: when you build a masonry fireplace from scratch, there is the basic building code specifying clearance to combustibles and such, and those are well known and static.

However, when you buy a factory-built fireplace, that same code calls for it just to meet the manufacturer's approved listing requirements. That's the trick for those metal prefabs - they need to be approved and listed as a conforming appliance - so that means the manufacturer must design it to meet ASTM, UL, NFPA, ANSI etc codes, and those codes are what a masonry fireplace follows anyway. What that trick does allow though, is a manufacturer can think up a unique design, as long as they have that design tested for compliance. They may have had to build-in tradeoffs, like a thicker glass screen, or double-wall construction, or thicker metal, or a taller hollow base, etc. to get an approved listing. And their installation instructions will be very clear about those requirements, here is a SPECIFIC MODEL of fireplace JUST AS AN EXAMPLE:

So if you'd like a combustible mantel, surround, or hearth, what you should do is find your model's instructions. That will tell you exactly your clearances. If you can't obtain those, then follow the basic masonry fireplace clearances to combustible materials as a fail-safe method.