One of those tasks that said waiting to start, just happened to start.
With my old client, it is exhibiting your behavior.
For 15 seconds it stays at 0, for the next ~4 mins it stays at .5%
After that, it seems to start incremental processing.
Since the task is a black box to me, it's not erroring, and I've never noticed this before, I'm going to assume it's a normal part of the task initialization.
These time estimations are just that.

Some are running fine, but sometimes tasks remain at 0.500% (and under 2 minutes, due to constant restarting) for over 30 minutes, and need to be aborted. I didn't find any pattern as to why this happens.

TL;DR -- Possibly given insufficient information, probably too much answer!

(I wish someone would publish an up to date, official "In order for us to help you..." FAQ somewhere...)

Troubleshooting this is like trying to diagnose a patient when one cannot even see them - all we have is a symptom or two and no way to perform tests! Despite that, you've already had some reasonable suggestions (including a nudge in the direction I'm about to go from IBM01902), but if they don't end up helping, consider the following...

As (unlike most other BOINC sites) WCG doesn't let us find out what hardware and software you are running on, there may be issues none of us have thought to mention as we have insufficient information. All the following can help:

• What sort of processor? A model number (e.g. i5-6600U or Ryzen 3700) is useful as CPU performance may matter
  
• How much RAM? How much of it is BOINC allowed to use?
  
• What operating system? (Even a version can make a difference in behaviour!)
  
• What version of BOINC client, and where did you get it from? (Some people even build their own!)
  
• Do you only run WCG BOINC tasks or are you multi-project? (That can make a big difference to task scheduling, which may make odd things happen!)
  
• If your issue is specific to WCG tasks, which sorts of WCG work do you run? (The task(s) showing a problem may not themselves be the cause of the problem!)
  
• Do you allow BOINC to use all your CPU capacity? (That can make a big difference for some [performance-related] problems!)
  
• Do you allow BOINC to suspend while your computer is in use?
  
• Do you have "Leave (non-GPU) tasks in memory while suspended" (sometimes referred to as LAIM) enabled?
  

As I said, some of that is in the user's profile at many BOINC project sites (if the user doesn't deliberately hide machine(s)!) - and it's one of the reasons troubleshooting is sometimes a lot easier elsewhere! (And, of course, it takes a while to get used to some of the quirks of BOINC so it isn't always obvious what might help us to help!)

In your case, my first suspect might have been items 8 (answered Yes) and 9 (answered No) if it weren't for the fact you said this started after a client update! If a task hasn't reached a checkpoint when BOINC suspends, it will have to restart from scratch if LAIM isn't set! And, as Falconet has pointed out, BOINC Client (and hence Manager) shows that strange behaviour when an MCM task starts,

By the way, an apparent inability to assess progress is not unique to MCM - many BOINC project applications only present an accurate assessment of progress at checkpoints (or at other major points in their code such as the completion of a sub-task), and different versions of the BOINC client have had different approaches to that; sometimes they start running a count based on the estimated run time and eventually "correct" it when they get a real progress marker (which has led to lots of users thinking a task has gone backwards when in fact it's just being accurately reported for the first time!) So it could still be items 8 and 9 in that list!

Hope your problem goes away (or, at least, that its cause is identified so you don't abort tasks unnecessarily!)

Cheers - Al.

I received this notification in the event log:

29/04/2020 19:29:54 | World Community Grid | Task MCM1_0162667_8991_0 exited with zero status but no 'finished' file
29/04/2020 19:29:54 | World Community Grid | If this happens repeatedly you may need to reset the project.