How long does it take botulism spores to germinate in the fridge?

This completely depends on all of the other factors involved in botulinum growth, not to mention the particular strain you're concerned about (there are several).

Salt, acidity (low pH), low moisture, and extreme temperature (low or high) will all slow botulinum growth significantly.

There are proteolytic and non-proteolytic types of bacteria. The proteolytic C.botulinum bacteria will never grow in the refrigerator - they cannot grow at temperatures below 12° C ^source. The non-proteolytic strains can grow at temperatures as low as 3° C. That is very close to refrigerator temperature so clearly they will grow very slowly - again, the exact speed depends on other factors - but they will grow.

According to other sources, the proteolytic strains (the ones that cannot grow in the fridge) are the ones that tend to produce gas and off-odours, so they'll be more easily detectable. They also have far lower heat resistance, so they are easier to cook away. But of course, if they've grown to a sufficient level, it's too late to do that.

As far as I know, there aren't specific guidelines for vacuum-packed foods, whether commercially packed or simply cooked sous-vide. I'd ask you to consider that botulism is not the only type of foodborne illness that can grow in the refrigerator. There's also listeria, salmonella, and possibly some others I'm forgetting about. Cooking (especially sous-vide cooking) doesn't kill every last one of them, just enough to make the food safe. By the way, listeria and salmonella are both facultative anaerobes which means that they can grow with or without air.

There's also the small matter of your actual refrigerator temperature. Although the theoretical temperature (4° C) is lower than that required for all but the hardiest of bacteria, once you move up even a single degree to 5° C there are many more kinds that can start to grow. How cold is your fridge, really? I've heard of some being as high as 10-12° C in parts! If your fridge temperature is even slightly high, botulism will be the least of your worries.

Honestly, given the incredibly tiny number of actual documented cases of botulism (less than a dozen per year in the U.S.) compared to the insanely high total number of food poisoning cases every year (1 in 4 according to some sources), people seem to place far too much emphasis on that particular species. I realize that it's one of the scariest on account of that whole "instant death" thing, but even if you could prove that your improperly-stored food is 100% free of botulism toxin, you could still get seriously ill from eating it. You're literally worrying about the least probable vector for food poisoning.

Bottom line, I'd strongly advise you to treat sous-vide food just like any other food in terms of food safety and freeze it if you plan to store it longer than 4-5 days. There are just too many variables at play to conclusively say otherwise.