Has there been research to see if cyanobacteria could live in high levels of CO2, like in the atmosphere of Venus ?
Because cyanobacteria caused the Great Oxygenation Event one might expect that they could !
Yes, there has been research. This paper asks and answers your question!
Here is the abstract of the paper. I highlighted the sentence that answers your question.
Cyanobacteria and similar organisms produced most of the oxygen found in Earth's atmosphere, which implies that early photosynthetic organisms would have lived in an atmosphere that was rich in CO2 and poor in O2. We investigated the tolerance of several cyanobacteria to very high (>20 kPa) concentrations of atmospheric CO2. Cultures of Synechococcus PCC7942, Synechocystis PCC7942, Plectonema boryanum, and Anabaena sp. were grown in liquid culture sparged with CO2-enriched air. All four strains grew when transferred from ambient CO2 to 20 kPa partial pressure of CO2 (pCO2), but none of them tolerated direct transfer to 40 kPa pCO2. Synechococcus and Anabaena survived 101 kPa (100%) pCO2 when pressure was gradually increased by 15 kPa per day, and Plectonema actively grew under these conditions. All four strains grew in an anoxic atmosphere of 5 kPa pCO2 in N2. Strains that were sensitive to high CO2 were also sensitive to low initial pH (pH 5–6). However, low pH in itself was not sufficient to prevent growth. Although mechanisms of damage and survival are still under investigation, we have shown that modern cyanobacteria can survive under Earth's primordial conditions and that cyanobacteria-like organisms could have flourished under conditions on early Mars, which probably had an atmosphere similar to early Earth's.
Thomas, D. J., Sullivan, S. L., Price, A. L., & Zimmerman, S. M. (2005). Common freshwater cyanobacteria grow in 100% CO2. Astrobiology, 5(1), 66-74.
I like this exobacteria theory question because they implement a strategy for answers that may go against or for the idea of out of space terraforming. Simply providing detail won't be enough in this case. Cyanobacteria are not very durable in Venus atmosphere. The temperature of Venus is of much higher average and they will be feeding of the atmospheric pollution as well causing an oxidative affect on the cell when too much co2 gives off oxides. But more importantly hydrogen buildup in the protein folds could cause inhibitory stress (prevents binary fission). So no I would not use Cyanobacteria as a space project. But please go against me if I'm false.