this worry about bettas seeing one another is something i have been reading on this forum since I joined. I appreciate that some folk will have had bad experiences where males can see one another.
however, i am going to express the other side of the argument so that you can weigh up both points of view and come to your own conclusion on the matter.
My tank is divided into 6 compartments using perfectly clear strips of glass, so each of the 4 males not in an end compartment has 2 neighbours that he can clearly see and interact with. my tank has been running like this for a number of months now, and i recently added a fairly young looking Crowntail. Not one of my males is showing the slightest sign of stress from being able to see his neighbour(s). Indeed, after a fairly short period of time the flaring has calmed right down to very little, the fish are settled and content and blowing bubble nests and barely flare at their neighbours at all, they just watch one another. I have found that they dont chase the shrimp and they are very sociable towards me. Once they realise they cant get at one another they chill out.
I'm not telling you its right or that being able to see other bettas is perfectly fine, I am simply relaying MY experience from having a tank divided with clear glass because I know that this side of the argument isn't often heard or put forward. Clear glass and visibility might not work for you or for everyone, but it can be made to work as my tank is demonstrating. I don't think its as big a deal as it can be made out to be. Also, my brother works in a tropical/marine fish shop and he built the tank, so at all times my tank is monitored by someone working in the industry and who has the appropriate industry training and he has assured me that all is good, which so far it has been.
again, not meaning to aggravate anyone, just expressing the other side of the argument so that you can decide what method best suits your needs/desires.
here is my tank for reference/illustration: