The new contract reveals their faith
The other side of the coin from this new deal is that while the Raptors apparently feared another team swooping in and signing Quickley, they weren't willing to risk that possibility because they want to keep Quickley on the team long-term. If they didn't believe in him as their surefire starting point guard of the future, risking an offer sheet is less scary. If they knew they would match anything, that possibility was more impactful.
The Raptors are 100 percent certain that Quickley is worth a contract like this and are committed to seeing him grow in Toronto. This deal was probably more than they needed to pay, but if Quickley blossoms into an All-Star candidate at point guard this will be well worth it, especially in the fourth and fifth seasons as the cap continues to rise faster than his contract amount.
There were likely trade offers on the table to bring back a package of first-round picks in exchange for OG Anunoby last season, but the Raptors instead chose to trade for players: specifically, one player in particular in Immanuel Quickley. That immediately put pressure on the team to pay up for Quickley; they couldn't lose him for nothing after making that investment.
They came through, as Quickley did nothing in his 38 games for the team to dissuade them from his upside. Quickley is a dynamic shot creator, a solid passer and a knockdown shooter, with good size not to get completely eaten up defensively; if he is your worst defender your team is likely fine.
The Raptors then made moves already this offseason to build around Quickley, adding a 3-and-D wing to partner with him in Ja'Kobe Walter in the draft and a pair of backup point guards who bring defensive intensity but clearly won't challenge him for the starting spot in Davion Mitchell and Jamal Shead. The Raptors are building a team around Quickley; he is the co-star with Scottie Barnes.
The Raptors paid more than they likely needed to with Quickley, but their faith in his upside means they won't mind this contract by the end. Given how well RJ Barrett played in Toronto last season and that they also added a prospect with the 31st pick -- and factoring in the massive new deal OG Anunoby signed with the Knicks, even more of an overpay than Quickley's deal -- the Raptors clearly feel like winners from their trade.
Now the onus is on Immanuel Quickley, to come back next season and beyond even better than before. The path is before him to reach his potential, and he has the contract to match. The Raptors had fear and they had faith; now we will see if those were well-founded.