BeOS only actually had a "database like filesystem" in very early versions, so most likely you're thinking of BeFS, the filesystem used in BeOS R5 (which was given away free) and in Haiku.
But all BeFS has in the way of being "database like" is arbitrary named & typed btree indices, chosen by the owner. You can have a btree of filenames, a btree of "sent by" email addresses, maybe one of file types for example. If enabled (which is the default) you pay for this feature with a significant perf overhead on operations because those tree indices must be updated, but if it's disabled (common for disks with lots of small files) you lose the facilities enabled by having such an index.
Compared to full text indexing, which was also popular on some systems at about the same time, this doesn't produce very impressive results, yet you're paying for it everywhere. No surprise then that even the text indexing remains a niche feature, I know people who care about it a lot and others who've never been interested.
It's probably one of those niche features like wall switches for floor lamps (a socket is run off the lighting circuit and switched just like ceiling lights, but a floor lamp is plugged into that socket). A few people love it, most people aren't bothered, so, it's usually not done.