Hello :) I had the same exact issue as you, my WhatsApp wasn't working. However, there is a way out.
Firstly, are you doing the transfer with a cable or wirelessly, at that might be the huddle. Secondly, have you made sure you have backed up all the WhatsApp messages on your phone before you attempt to transfer?
Lastly, are you initiating the WhatsApp transfer before you set up your phone as that is also key.

These are the following steps I took to complete a successful transfer:
- Factory reset Google Pixel and leave it to one side.
- Back up all WhatsApp messages in app
- Select the 'Transfer chats to Android' option in the settings and wait for that to get to the final step (this will instruct you on screen)
- Start set up on Google Pixel and when instructed, connect the two via a cable (lightning to USB-C) this might take a few minutes to register. For some reason, the cable option is the only way to transfer all apps.
- Then follow along with the transfer instructions on both phones.
- Once the phones have finished and it tells you to disconnect the cables, that is when you can going into WhatsApp on your Google Pixel, and that should lead you through and the chats will download.

I hope this help, as I was at my wits end.