Is there a route-planning tool that clearly indicates tunnels?
None of the bike routing services I have tried or asked about know about tunnels.  They don't even mention them on route/cue sheets (unless presumably the road name has "tunnel" in it) so a text-search fails too. When it comes to scanning the route for tunnels, OpenStreetMap (standard or humanitarian layer) is clearer when zoomed out to a reasonable scale than Google maps or OpenTopoMap.

If you like watching video and your route is on Google Streetview, this video player for Streetview (link is a section of my route) will indicate tunnels, but it takes more patience than scrolling through the route.