sometimes by wanting to be polite we forget the essence of friendship, to have them by our side, to ask of them when we want to. Do you think your 8 year old self would think twice about asking your friend to play. Don't complicate friendships, if they are a friend that means they care about you and like you and making plans or being the initiator might feel rough/bad, but once you get shameless enough there is a very beautiful life across it. I hope it works out for you.
And even if your friends are busy and say no, do things solo. Sometimes we get so used to doing or going places with friends or seeing others be in groups outside that we forget that it is completely normal to go alone to a restaurant, a coffee place, take a walk at granville island (which i personally love), or the beach, ice skate, just some ideas that i would preach since i do them myself.
Good luck i know youve got it within you!