The SPD tends to be more socially conservative than the Greens (although the party base is extremely mixed). They only proposed a very cautious experimental legalization program during the election and mostly didn't talk about it. They're likely seeing this as a cheap win they can still pin on the other coalition partners if pushed on the issue by conservatives. After nearly two decades of grand coalitions, they seem to mostly let the other two partners do what they want for now.

The FDP may be market extremists but they've been using legalization as a major ticket to attract younger voters for decades now. Their shtick has basically been doing politics focused on big businesses and the extremely rich while marketing themselves as an attractive option for young voters by pushing reasonably popular progressive policies (as long as they don't interfere too much with the economy). Their primary motivation for legalization is likely economical (since the tobacco industry has been pivoting towards cannabis for a while now since lobbying for less tobacco regulation stopped working decades ago) but the kids will think it was a principled stance towards progressivism or liberty or something, so it's a double win.