I have encountered this several times by new users asking me how to do it and I know this will be out of date in a month it will be of extreme convenience to me and all other users who ask again.
Find your favourite avatar (It could be in any world with the CVR component "CVR Pedestals" in them.)
They look like this:

Next you will need to click "details" on the avatar pedestals you want to save into your account for future use.

Once you click it, you will need to click the "Favourite" button within the UI

Once you click the "Favourite" button, you will be prompted to where to save it to. So you save it to the default category:
The custom category selected: Red Highlight
After you have selected your default category, you must apply those settings at the prompt below, you will then be prompted with the message "Settings Applied":
Apply button: Yellow Highlight

To find all avatars you have favourited throughout the adventure you will have in CVR, they will be located here:
In the avatars tab and the default category tab:

I hope you all had fun reading this! I will update the tutorial once the new UI changes come out but for now, it will be useful for anyone who doesn't wanna explain it again. If you have any suggestions or tweaks, please reply to this or personally message me on discord at MrTactical#8167