Would it be possible to add support for linear gradient colors in drop shadow effects within Figma?

The reason is in how the effect is built, not in a missing colour picker. A drop shadow in Figma is not a shape you can paint — it takes the layer's own alpha silhouette, blurs it, and tints the whole thing with a single colour. There is one colour slot per effect because there is one tint being applied to one mask. A gradient would require the shadow to be a fillable object rather than a tinted mask, so this is a deeper change than adding a gradient control to the panel.

Two things that work inside Figma today.

Stack several drop shadows on the same layer, each with its own colour and offset. Figma composites them back to front, so a warm one nudged one way and a cool one nudged the other reads as a two-tone shadow. The part that catches people out is that the alphas add up across the stack. Each shadow has to sit much lower than you would set it on its own: past roughly 0.24 of total alpha the result stops reading as depth and starts reading as a grey box, and below about 0.04 a layer contributes nothing you can see. Budget the opacity across the whole stack rather than per shadow, otherwise the second colour just muddies the first.

For an actual gradient, duplicate the layer, send the copy behind the original, fill the copy with the gradient you want, then apply Layer blur (not Background blur) and offset it. That gives you a genuine gradient-shaped shadow with full control over the ramp. The cost is that it is no longer an effect you can save as a style and reuse across a library, which is usually why people fall back to the stacked-shadow version even though it is only an approximation.