Ultimately what stopped them ( and everybody else - let's face it it wasn't just the soviets ), is it's a bad idea.
I think you way over estimate how hard the knowledge bit is in a biological weapon ( if you just want to kill indiscriminately - specific/controlled targeting a whole different ball game ).
The barrier is motivation and kit ( though the kit is much easier to access that say the stuff you need to build a nuke ).
The idea that all that's stopping some disaffected Joe sitting on his sofa at home and suddenly deciding to make a biological weapon is he can't get a set of instructions from ChatGPT is to miss the point.
Ultimatelty it all comes down to are you motivated enough - if you are then the knowledge is out there with or without an AI summary.