I've saved some screenshots of the Whitney webcam from last year and compared them to the pictures from today. Last year was a heavy snow year, so there was slightly more snow on and around Whitney 11 months ago (7/13/19) than there is today (6/13/20):

So, what are the trail conditions like? It's hard to get firsthand accounts since the trail is still closed, but it's possible to make a good guess by looking up last year's trail reports from mid-July:
7/10/19 day hike without spikes or poles, portal to summit in less than 6 hours: http://www.whitneyzone.com/wz/ubbthreads.php/topics/55704/july-10-day-hike-from-whitney-portal
7/11/19 summit, most people in that group didn't use microspikes: http://www.whitneyzone.com/wz/ubbth...nt-conditions-mt-whitney-trail#Post55714
7/15/19 day hike via the switchbacks, cables could be safely passed: http://www.whitneyzone.com/wz/ubbth...19-whitney-main-trail-to-summit-day-hike
7/15/19 pictures of the cables: http://www.whitneyzone.com/wz/ubbth...nt-conditions-mt-whitney-trail#Post55736

Based on those trip reports and the webcam images, I think it's pretty safe to say the following for the main trail as of today (6/13/20):
- No snow until Mirror Lake
- Some patches of snow from Mirror Lake - Trail Camp, but nothing that requires mountaineering gear or route finding
- A few areas of ice, snow, and running water on the switchbacks. However, the switchbacks are much safer, faster, and easier than the chute.
- There's not enough snow to glissade down the chute
- The cables at the switchbacks are a bit sketchy but manageable
- Crampons and an ice axe are not needed anywhere on the trail
- Microspikes will help, but it's possible to summit using only boots and poles
- You may get your feet wet on the creek crossings, but everything above your ankles should remain dry

However, crampons are still required if you're heading up the mountaineer's route. Here are trip reports and pictures from July 15-16, 2019: