This is novel. On login, the left-hand panel sizes itself incorrectly like so:
Selecting Properties and either increasing or decreasing the panel width triggers it to size and place things correctly, per #2. Note that the panel is the same width in both: this isn't a case of it not EVER being able to size things correctly, just not being able to do so right away.
I'm afraid this may be a bit irrelevant, but nevertheless, I've long ago dropped any attempts to make left side vertical panel with native/standard methods due to everlasting problems.
The only cure I've found is Cairo Dock. It allows me to have left side panel exactly as I want it:
Have you tried killing the panel and then reloading it? This restart might reset the item placements. If it does, you could emply a hacky solution by adding a "killall mate-panel" command to your startup list
I haven't, but since this is a regression in 19.10 it shouldn't be too hard to actually find and fix it, hopefully.
Restarting the panel is a clever idea, but since the bug shows up AT start and is fixed by "resizing" it after that, my guess that'll just perform the same way as starting it in the first place. I'll try it out next time I'm upstairs though. I'll also try saving and reloading the panel setup and stuff like that.
The reason I asked is because, in my experience, a lot of the problems at startup are due to a "race condition". Which is where too many processes are competing for processor resources and bits start to "fall off the edge", as it were.
The above being the case, I have found that if I have a problematic process occurring at login. I usually set it to manually load in some way via a startup command, often with a delay built into the command. So, for example, I might make a little script like the following:
sleep 2
killall mate-panel
mate-panel
And then run that as a startup script at login
However, I also think you could resize the panel using a script with something like:
gsettings set org.mate.panel.toplevel:/org/mate/panel/toplevels/bottom/ size 45
Obviously, you would need to change the above command slightly to reflect which particular panel you are referring to and the specific size.
This turned out to be a TERRIBLE mistake. 
I saved the panel layout (not quite the same as the one above, but close enough for this), switched to one of the built-in layouts (SUSE, chosen at random, since all I wanted was "not what I have"), and switched back to mine. What I actually got back was two panels that were mostly empty, with EVERY setting for EVERY applet wiped out.
The MATE Menu and Control Center were missing entirely, but that was the least of my concerns.
System Monitor was back to CPU-only and default colors (which I'll come back to). Only 1 CPU was being monitored. The correct names for the HW sensors had been replaced with "temp1" etc. My location (for Weather) was gone. And so on. You get the picture.
I tried killing and restarting mate-panel, and even logging out, just in case those would get it to recover, but no such luck.
It took about 45 minutes to get everything reconfigured. Not happy. I know it's still Beta, and I signed up for problems when I installed it, but ugh. Then I saved it under a new name and tried to load that one, and that barfed in the same way so I gave up.
Oddly enough, the panel from 16.04 has been loading fine, aside from the bug that started this thread. I should have quit while I was only slightly behind... 
I've got the config files, and I'll dig into them over the weekend.
On a related note: mate-panel needs to save the config files under the user's home directory, not in /usr. How is a normal user expected to copy them between machines, or restore them from a backup?
System Monitor I actually COULDN'T get reconfigured properly, because, wow, what the @#$% is that color chooser supposed to be?! It's not just dumbed down to near-uselessness compared to the old one, but it's broken AF on top of that.
Can we please have the MATE one back, with the wheel and the eyedropper? I don't care if it only works in the MATE apps. "But it wouldn't be consistent then" is irrelevant when Option B is "utter garbage".
