For a number of years we allowed Russian spy planes to fly over our nuclear bases. That ended in November 2020. In return our planes flew over their nuclear silos. It was a way to verify compliance with an arms treaty.You do NOT Know if any damage was done. Militarily that is unknown. What I do know is allowing an object to traverse our Country could pose a danger. Will it? Maybe, maybe not. The point is, it was a risk. One that made our Country appear weak at a time when we need to be showing strength.
Treaty on Open Skies - Wikipedia

The point being that they knew where our silos were...you can be sure they shared that with the Chinese. Knowing where they are is irrelevant. They can never get a nuclear first strike to the point where our missiles would still be there if they were to launch.
Add to that our subs would pulverize China on a full scale war.
Lastly, do you think we couldn't jam their transmissions from the balloon? I think it impossible that they gleaned anything useful from this.