What buttons enter the clinch in UFC 6?

Orthodox: Triangle+Circle (PS5) or Y+B (Xbox). Southpaw: Square+Cross or X+A. Press them together.

Why does clinch come out as a takedown?

You are probably on Streamlined, or you hit the takedown face button. Check Control Assist.

No. Close with a step or a punch. A walk-in clinch is a knee or a stuffed entry.

They read a naked clinch the same way they read a naked shot. Step or punch first, then take the lock.

How to enter the UFC 6 clinch: Orthodox and Southpaw buttons on PS5 and Xbox, and why you enter after a strike.