All of them has the ladder fastened to pieces of solid wood fixed to a frame, rather than the BILLY bookshelf. As you suspected, particleboard BILLY is too flimsy to hold up a heavy track.
The BILLY bookshelves themselves should be fastened onto the wall. The backboard is not sturdy enough so you will need a combination of L and corner brackets to secure the units to wall studs (if on a drywall).
IKEA BILLY bookshelves with rolling ladder
In the photo below, Doug stacked short BILLY bookshelves on top of the tall ones with solid wood between the units. The piece of solid wood is where he fastened the rail. See the details here.
The Makerista also has lovely built-in IKEA BILLY bookshelves with a library ladder.
Hope it all goes well. Let us know what you end up with finally.
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