Shape shifting tables are actually quite common! There are quite a few types:

• Tilt Top Chair-tables. Hinged closed, it's a table about the size of a poker table. Hinged open, it's an armchair, with the tabletop forming the back.
• Drop-leaf tables. I've seen these in several shapes but the typical pattern is a long, thin rectangular table with hinged panels that can be folded up to extend the top. They can be folded to as little as 18 inches wide and stowed against a wall, you can open the free side with it still against the wall to seat a few people, or you can slide it away from the wall, open both leaves and have a full size table. Stowage of side chairs is a separate issue. The shakers were fond of drop-leaf tables, and made some truly huge ones that could seat a dozen people or more when unfolded, but would stow very efficiently.
• Extending tables. My dining room table is one of MANY examples, you'll find them all over the United States because it's objectively the worst of the lot: The long apron rails aren't continuous but attached by a slide mechanism. The tabletop is split in half, so you get two table halves that can slide relative to each other. A gap can be opened wide enough to admit one or two lift-out sections to make the table longer. My dining room table can collapse to seat 4 around a (mostly) round table or extended to seat 6. All the additional hardware plus the two extra apron rails necessary make the table heavier than it should be, the slides never work right and if you prefer to have it collapsed, where do you stow the leaves? I guess with the two side chairs you nearly never use.

I have one, my parents have one, and I just found out that the person I'm dating has one (technically her parents have it). So they must not be too uncommon.

I have one! It goes from 2 ppl to 6 people by extending. Found it while thrifting.

Huh, I've only seen dining room tables that could expand using table leafs. The only time I didn't have that was when I lived away in college because why would we have that if we just ate on the couch lol