If the tables were turned, and you had a male 'best' friend that regularly rang you, and you saw him once a week, he texted you, and you had an emotional connection with him even though he had a gf and you had a bf - How would you feel? If you are yanking two men along by their chain then you would probably be like the cat that has the cream. How would your boyfriend feel about this man?
It's ok being kind etc - all lovely qualities. But it can depend who is the 'injured' party at the end of the last relationship. Who is hoping to rekindle a love or gain an unrequited love? Why would you hang around waiting for someone to make their mind up and to decide if they want to be with you? That answer should be blindingly obvious. Finding someone who ticks one or two boxes just because they are in the right place at the right time, plus they are useful for sex is an all too common scenario. A convenience rather than a mutually passionate relationship.
In either case you can end up being played and 'used' as a useful idiot. A staging post until a better offer comes along. Then you won't see them for dust. When that happens you will wonder what you did wrong. The answer is nothing. You have a choice to be brave and get out of this relationship where there is no real commitment toward you. Your bf certainly has no real consideration of how he is making you feel. You can talk about it, and explore how you both view your relationship. But then you are left feeling that you have poured cold water onto the extra emotional relationship stuff. Maybe after saying something like he is 'staying with you' because you made a fuss. In short you are together for the wrong reasons. That is not a good start.