The Entity Token submodule for Drupal 7 provides support for chained tokens, so they can be used with entities referenced by fields. However, Backdrop's implementation of entity_token is very simple and doesn't include that, only
chained url and
original tokens are included.
This whole feature has been already requested in https://github.com/backdrop/backdrop-issues/issues/1440. However, that doesn't seem a straight-foward implementation. It's relying a lot on Drupal 7 Entity functions, such as entity wrappers and other utilities Backdrop doesn't have, or use the same way.
My approach here would be to start providing something simpler and more widely used, a taxonomy term reference field chained token.
For example, we can use the parents path in an alias pattern
[node:_field_taxonomy_term_:parents:join-path]. We can provide this from the Field module.