So truthfully, DnD as a system doesn't really encourage role playing until you experience it. Then the thirst for more of that is why we do it.
The stats are a kind of fun. Building your character and playing them is all good stuff too.
But here's the rub, role playing is where it switches from a co operative board game into something that has lasted for so many decades.
How? That's mostly up to you really. I found that being contrary in some things works. For example, in my current game, one of my players is a spirit shaman. He refuses to use violence as the answer to any situation we didn't either try to talk our way out of or are certain will end worse without our intervention. He's explained this to the group as the spirits of regret he has to listen to all the time ruin his day and he won't be involved with doing more of that.
He has literally gotten in our way when we decided to intervene on some trolls before, because they hadn't seen us; we didn't talk to them and they hadn't killed in front of us. So why kill them? Why ambush them at all? We could just sneak past.
He isn't ruining the fun of others, he isn't making a character that has no reason to be out adventuring, common missteps. Yet his disagreement has made us have to perform mental and verbal gymnastics to accomplish our goals and it adds to our story.
The druid from the same party started with no idea of what his personality would be like, deciding he would develop it as he adventured. His animal companion (whom he lavished attention upon) died rather brutally to some bandits in a keep about 3 months into our campaign and he went into mourning for about 3 months. He didn't stop adventuring or anything but just stopped scouting unless asked. He didn't perform perception checks, didn't go out drinking. He simply existed and lifelessly performed basic stuff for the group, to the point where when surrounded by 3 enemies, he didn't call for help. It was disturbing in a way but rping getting him out of his funk meant we actually hunted down the bandits in the entire country, wiping out that organization to the last man for him... and then he became a brutalist, maximum force always type of character who kept a distance from his new animal companion. He even requested that it be stunted a little in it's growth to reflect his refusal to allow their connection to deepen. Seems wild to request lower stats, but the rest of us got the message. He was changed and scarred.
DnD is surely a game with rules and it is fun to do the dungeon crawl, but there's lots to discover in the cracks between too. The trick is to not be an infinitely brave role like tank, but rather a person first. A fighter can feel fear and refuse to move forward. A cleric can feel someone hasn't followed the tenants of their faith and refuse to heal them for a while.
Find the person in your character, and give yourself time to let that happen rather than trying to force it.