I might run 3-4 claude sessions because that's the only way to have "multiple chats" to e.g. ask unrelated things. Occasionally a task takes long enough to keep multiple sessions busy, but that's rather rare and if it happens its because the agent runs a long running task like the whole test suite.
The story of running multiple agents to build full features in parallel... doesn't really add up in my experience. It kinda works for a bit if you have a green field project where the complexity is still extremely low.
However once you have a feature interaction matrix that is larger than say 3x3 you have to hand hold the system to not make stupid assumptions. Or you prompt very precisely but this also takes time and prevents you from ever running into the parallel situation.
The feature interaction matrix size is my current proxy "pseudo-metric" for when agentic coding might work well and at which abstraction level.