Azure – Is Azure Temporary Storage tied to different VM types always local & SSD based

ln -sTf /mnt/pgsql_tmp $PGDATA/base/pgsql_tmp  # did you get that correct?
chown -R postgres              /mnt/pgsql_tmp
chmod o+x    /mnt          # note: no -R,  this turns 750 to 751 for /mnt only

The effect:

 su - postgres
 echo 1 > /mnt/file   # fails
 ls   /mnt            # fails
 cat /mnt/anything    # fails
 echo 1 >  /mnt/pgsql_tmp/file   # works
 ls /mnt/pgsql_tmp               # works
 cat /mnt/pgsql_tmp/file         # works

The chmod o+x means to give [o]thers the +e[x]ecute bit, which gives them a permission to traverse across /mnt into any subdirectory. Other permissions are not necessary for /mnt only for /mnt/pgsql_tmp

As your issue report said,

Your application was recycled due to an intermittent Azure infrastructure issue while accessing remote file storage.

Azure need infrastructure to be upgraded and keep your resource healthy at the same time. So, it recycle your Apps at random to reach that .

Is there anything I can do to fix this? Is the suggested local cache safe to use on a content manged site?

For now ,we should wait azure finishing this upgrade. We cannot fix that due to it's about Azure infrastructure issue. This would not cost too much time.Using Azure VM or Web App service is quite safe to hold your Apps on Cloud.

App Service Local Cache can be used for Azure Web App Service. According to your issue , You needn't use this feature because your Apps is running on an Azure VM . After this upgrade , all your apps would be running well.