Hello Ziandri
Harder Kulm is operated by Jungfrau Railways, not SBB.
Yes, the funicular is the only transport provided, otherwise you would have to hike.
You can purchase the tickets at BLS train station, Interlaken Ost instead of at the base station of Harder Kulm. On sunny days, there are crowds, especially until noon.
I would not purchase the tickets in advance. In case of bad weather, like today, the mountains are not visible as they are covered in thick clouds.
I, personally, prefer Schynige Platte. Identical views, less crowded, more Swiss, and it has even an Alpine Flower garden.
Kind regards,
Roland