tree-diff: remove the usage of the_hash_algo global

tree-diff: remove the usage of the_hash_algo global

emit_path() uses the global the_hash_algo even though a local repository is
already available via struct diff_options *opt.

Replace these uses with opt->repo->hash_algo. With no remaining reliance on
global states in this file, drop the dependency on 'environment.h' and remove
'#define USE_THE_REPOSITORY_VARIABLE'.

This follows earlier cleanups to introduce opt->repo in tree-diff.c [1][2].

[1]- https://lore.kernel.org/git/20180921155739.14407-21-pclouds@gmail.com/
[2]- https://lore.kernel.org/git/20260109213021.2546-2-l.s.r@web.de/

Signed-off-by: Shreyansh Paliwal <shreyanshpaliwalcmsmn@gmail.com>
Signed-off-by: Junio C Hamano <gitster@pobox.com>