How can I make haproxy route requests based on URL substrings?

You want to use ACLs:

backend be1 # this is your default backend
  ...
backend be2 # this is for /tag-02 requests
  ...

frontend fe
  ...
  default_backend be1
  acl url_tag02 path_beg /tag-02
  use_backend be2 if url_tag02

Section 7 of the HAProxy configuration guide has the details on ACLs, but you have to know the magic use_backend incantation hidden in section 4 of the guide to know what to do with the ACLs.