Two accounts in my device looks like interlinked

I have created two profiles in my mac for office and home purpose.

I am using two profiles one signed in with a apple ID and one without signed in but I do not need same applications in both profiles

I downloaded HomeBrew in new profile and HomeBrew from my old profile got removed.

I want to use both the profiles independent of each other so I can install different softwares

in both and adding or removing package or app in one does not affect the other.

Can someone please help me understand how this can be done