A closed-off dell ringed entirely by mountains is smothered in smoke at 900°F from a dragon. After suffocating the forest, a magical barrier seals them in. It is invisible but doesn't allow airflow with the outside world. It bulges up or inward to maintain pressure equilibrium, but nothing escapes. The barrier is a perfect conductor of heat and light.
Several creeks trickle in from the mountains and leech into the soil, the barrier doesn't stop this.
This is a temperate climate with a dense mix of deciduous and evergreen trees; the season is late spring with optimum daylight. A light morning fog covered the forest at the time of the attack, when everyone was asleep.
The smoke is normal wood fire smoke with carbon monoxide, carbon dioxide, and soot. It comes in rapidly but not instantly, the dome traps most of the smoke in before it can be drawn out by convection (50% air is displaced, again).
Survivors if any will need to find air pockets and restrict their breathing, but that isn't in this question. I plan on having a few survive. But the question is about survival of the forest which spans 300 acres and is at least 50% depleted of air when sealed. Estimated air is 20 million m$^3$
If this dome stays and the forest survives, how long would it take for the dome to become irrelevant (the oxygen has returned)?
I know the CO$_2$ will increase vegetation yield linearly with percentage increase, but it has to first absorb the heat energy of the smoke within the existing mass, which may wilt green leaves and delay replenishment.
Balancing the several factors makes this trap a problem, where I want the animals to be endangered but keep the forest alive. The dragon is protecting it by smothering the animals. The listed magic is the limit that can fit into the plot: Smoke-breathing dragon, and a magic barrier. No other magic can apply. Will the forest ultimately survive (or even thrive)?