I read the “tech” like in technology: stra-tech-ery.

Though at first I misread it as stratrechery which has other connotations!

This is the correct answer, but I always read it as "straight-cherry' in my mind.

Ben Thompson cohosts a podcast [0] that comes out very irregularly, but is a true gem. He says "stra-tech-ery" there, so you are correct :)

[0] https://exponent.fm/

Yeah, but for some reason I prefer "stra-tuh-cherry"

Exponent.fm has been dead forever. He has three paid podcast now.

I assumed it was derived from "strategery". (strə-TEE-jər-ee)

https://en.wikipedia.org/wiki/Strategery

It is, but Ben pronounces the "tech" in the middle as it's pronounced independently.

Right, a reasonable person would understand that in order to map the pronunciation of "strategery" to "stratechery", you would substitute "TEK" for "TEEJ".

I thought it was a one word combination of "strategy" + "tech"

Stra-teachery.

My brain misinterpreted it at first and now it's too late to fix it.

I always hear it as Will Ferrell's GWB saying "strategery" instead of "strategy." I know it's incorrect but that's my brain for you.