pool selection based on specific context path and certificate termination on each member server

If you want the default pool assigned in virtual server configuration is assigned in the switch default statement, you can store first after TCP handshake:

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

when HTTP_REQUEST {
    switch -glob [string tolower [HTTP::uri]] { 
        "/health/v1/*" { pool uat_pool } 
        "/check/v2/*" { pool qa_pool } 
        default { pool $default_pool } 
    }
}