Yeow! Not a good feeling, Brian, but not hard to fix.
You are in an area where it rains, at least occasionally, so I would recommend that you not simply reaffix the stack base to the chimney. You need to add a mortar “crown” to top the oven’s chimney first.
I wrote about it in this post from earlier in 2023:
Your situation isn’t as dire, because it looks like your chimney is in good shape. So I’d use a sharp blade (like a widget or glass scraping tool) to scrape off the old silicone sealant. Then follow the instructions in the thread above to build a crown to cap the chimney. It will cure as you build new fires, so just let the mortar set to the touch, then reattach your chimney with new silicone sealant per the oven instructions.
As for attaching it, yes, you can use TapCons to attach the DuraTech base to the chimney crown. @BrickWood says that he stopped including that step because some builders were careless and ended up cracking the chimney brick!
So, use a relatively small TapCon anchor/bolt set, drill very carefully—straight down, and to the exact depth specified on the package—and don’t over-torque the bolt. The silicone is still doing the primary job of attaching the base to the crown, and the TapCon anchor is stabilizing it.
I feel more confident recommending this to you because you will be adding the missing crown, which will help keep the underlying firebrick from cracking. But again, please be careful.
Good luck, and please post with further questions and photos of the completed repair, Brian!