Recreation.gov has been very good about announcing closures of federal parks, though most of that has been over budget stupidity.
If there are wholesale closues, I'm sure it will appear there quicly. While the individual USFS campground may not be on Recreation.gov due to lack of reservable sites, some CG in that national forest is almost certainly on the web site and closure notices for the forest will be posted there.
If all else fails, call the forest headquarters and ask.
Edit: I just checked on some campgrounds in Washington state and they are taking reservations and expect to open on time.
Also, we are full-timers, kind of hard for us to stop going to campgrounds. But we have decided to not attend a campout of a group we belong to this coming weekend, or a state rally the first week of April.
Not over fear of catching the virus, but we looked at the risk factors. Both over 70, high blood pressure, one with Type 2 diabetes. If we are exposed, we have a high risk of developing a very to most severe case.