IMO the creak is probably caused by a "gap". The threads in the frame aren't exactly the same size/shape as the threads on the BB. The difference is probably almost microscopic. But it's enough to allow a rocking movement.

Repeated movement will push soft things away, like grease, anti-seize, etc.

As a "solid", Teflon tape will occupy the gaps and cannot be pushed aside, and will neither decompose, nor wash out. Think about why plumbers use it.

Wrap the BB with one spiral and screw it in. If it screws in easily, remove it and the Teflon tap. Apply two wraps (or 1.5 overlap) and try again. Repeat this process of increasing the overlap and thickness until it takes a good amount of effort to screw it in. Not enough to F things up, but it should require a firm effort to turn it all the way from the first turn to the last.

The C&V guys swear by this. When I think about a 40 year old bike that has seen a gazillion miles and had the BB replaced many times over the years it makes perfect sense to me.

Like I've said, I've never done a BB before.

But I have used it on motorcycles where the male/female threading interface felt poorly matched (sloppy) and I was worried about the fastener coming loose.