Leaking struts, how serious is this?

I would agree with your mechanic that the repair work is not urgent. The possible consequences, including rollovers and tire wear, apply to struts that have outlived their useful life and are no longer performing their intended function. You would know it by a bouncy ride.

The $2000 price tag, however, seems way out of line. I don’t know if there is anything special about Subaru struts, but a similar job on other cars goes for half that price or less.

In any case, there is no reason to go to a Subaru dealership for this repair. When you are ready, visit the independent repair shops and ask for a quote. Also, you may not need to replace all four struts. Maybe you only need to replace a single pair. Ask to see which one(s) are leaking.