Algae terrarium works without CO2 and in pressured room

U could build algae terrarium and it would produce oxygen even if there are no Carbon Dioxide around and even if room are full of 7kg oxygen at any tile already. And seems that if there would be even more.

Also in reality algae used C from CO2 to reproduce themselves and for inner processes only in the light. And they consumed it from water, not from air.
And they are doing it only in the light if there are no light they just breath the Oxy and emits Dioxide. Cause this is how photosynthesis works.
Algae is kinda natural water filter. Would be more logical if they would used polluted water in the light.

Ofc also we have Crassulaceae acid metabolism when the phases are reversed. But this way is inherent in plants of deserts.