There are a few steps I take that are not all about them, but add some personal connection to the world.
Have helpful NPCs be related to their backstory
Often when they seek someone out for help with a quest or adventure I'll make them connected to their backstory. If someone is a noble who rejected their house to adventure say, I might have a noble cousin who knows a lot about werewolves as a contact, so they can reflect on whether it was a good idea giving up nobility- they can see the pros and cons of staying as a noble, and help their cousin rise or fall in the world.
I've found this often helps add some emotional connection for players. You can overdo it, and if everyone is a relative it looks silly, but I make sure to include one or two connections each session and it's fine. For characters who are very charismatic in familiar locations I can make more connections, since they would know everyone.
Have an enemy or friend trigger a fear of the PCs.
Often they'll have something like they hate religion, or magic, or rich people, or poor people, or any of a variety of groups. It can be fun to set up an encounter to play off that. You either have an enemy who is satisfying to kill as the embodiment of their fear, or an ally who is helpful who embodies whatever faction.
You need to balance this carefully- if they hate the group too much they may disrupt your campaign. I have had players go berserk against someone who was meant to be an ally.
Interconnect organizations they're in to major quests
If they are a part of major organizations I often make them interact with players on quests. For example, if they're a part of the church, when they raid a goblin fortress they might be joined by paladins of said church. That's a chance for them to see their organization changing the world, interacting, and making choices.
It's important to establish alternative goals- perhaps the church is trying to suppress worship of a goblin deity, or hide some dark secret like that their god had a child with the goblin deity. If their goal is looting the dungeon and take loot away from them then the players may start to hate having a backstory which isn't good. Having an organization the player hates can work for competing for loot.
How regularly you do this depends on how widespread the organizations are and the types of quests.
Have a unique skill or favoured situation for a PC
Suppose a PC has some obscure skill like pottery. Once every few sessions you can include something related to it. The dungeon has some rare valuable pottery. An NPC is absurdly into pottery and likes people who relate. There's some sort of trap that can only be solved with detailed knowledge of pottery types.
If you do this too often it looks silly, but it can be a rare treat for obscure skills.