Adjective of or relating to "ember(s)"

I thought perhaps embery could be a word, but it isn't. Is there such a word? Here's the sentence I intend to use it in: He reached into the fire and grabbed an (embery) log.

I think smoldering may suggest the idea you want to express:

burning slowly without flame, usually emitting smoke.

He reached into the fire and grabbed a smoldering log.

(Collins)

From Haunted America, By Michael Norman, Beth Scott

Seated next to the faint glow of the fireplace's single smoldering log, Kim occasionally glanced through the mesh screen of the open fireplace into the lobby.

I don't think that embery would be misunderstood, and it does follow the common method of turning some nouns into adjectives, but it might look strange.

It's something you could use in poetry, or enclose in quotation marks (to indicate it's been made up).

But you could also make use of -like:

[Merriam-Webster]
-like adjective combining form
: resembling or characteristic of
// bell-like
// ladylike

In the sentence in the question:

He reached into the fire and grabbed an ember-like log.

Again, while probably not something to use in a formal context, it should be fine in most informal contexts.