LB::server pool returns empty string

I need to switch between two different pools, based on the url. I found the following pattern in several answers:

when CLIENT_ACCEPTED {
    set default_pool [LB::server pool]
}

when HTTP_REQUEST {
    if { ... } {
        pool $default_pool
    } else {
        pool other_pool
    }
}

However, LB::server pool always returns an empty string. I have configured a default pool and the behavior appears if a oneconnect profile is set as well as when no oneconnect profile is set.

I am on version 11.5.3.

Edit In response to Kai Wilke

: 1 - LB::server_pool =
: 1 - $default_pool =
: 2 - LB::server_pool = /Common/DefaultPool
: 2 - $default_pool = /Common/DefaultPool

When I attach an OneConnect profile, the pool is not reset to the default one. Resetting it to the default would solve the problem though. Independently of a OneConnect profile being present I have to reset the pool explicitly to the default one.

Edit based on the assumptions by Brad Parker

I changed the code to this pattern:

when CLIENT_ACCEPTED {
    set default_pool ""
}

when LB_SELECTED {
    if { $default_pool == "" } {
        set default_pool [LB::server pool]
        log local0.debug "1 - LB::server_pool = [LB::server pool]"
        set default_pool [LB::server pool]
        log local0.debug "1- \$default_pool = $default_pool"

        pool DefaultPool

        log local0.debug "2 - LB::server_pool = [LB::server pool]"
        set default_pool [LB::server pool]
        log local0.debug "2 - \$default_pool = $default_pool"   
    }
}

when HTTP_REQUEST {
    if { $redirect } {
        pool EMDRA
    } else {
        pool $default_pool
    }
}

The behavior remains the same: [LB::server pool] returns an empty string as long as I haven't set a pool explicitly by calling pool some_pool