How to pass field value to referenced node template?
TL,DR: No.

Long version:

Conceptionally entity render arrays are self-contained, cachable units. The Drupal way would be either preprocessing and a custom cache context based on the referencing node, or a views block with a contextual filter.

But IMHO both ways are terrible workarounds, your Twig snippet {% include ... with ... %} is the better technique.