I understand that this would be a helpful feature, however this option is not available on Nest displays. Check out this guide for more detailed information about liking music via YouTube Music.
In line of this, we want to encourage you to send feedback from your end and we’re hoping for all the possibilities by taking our user’s feedback and suggestions.
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As long as you have a YouTube Music subscription and your personal results is enabled on your Google Home app, your liked songs will create a playlist. If you want to play it, you can use the command "OK Google, "Play my liked songs," "Play my liked music," or “Play my thumbs up”.
Hope this helps.