It’s a good idea to have tagging for tunnel portals. Here’s a particularly elaborate example which has its own wikidata entry.
This is currently tagged as an archeological site, resulting in this weird rendering:
I’m not convinced by entrance=yes, since this duplicates the meaning of portal. We don’t want people adding entrance=yes to any tunnel entrance.
I’m also not convinced by portal=building as the vast majority of tunnel portals are not buildings in the normal sense of something that has a roof.
man_made=tunnel_portal has the advantage of being clear and specific. Otherwise there is an overlap with man_made=adit.