If I play Timewarp, do I get a point for holding on my extra turn?

Yes — your Time Warp extra turn is a full turn, so you go through your Beginning Phase and score holding points for each battlefield you control that you haven't already scored this turn (Core 735, 315.2.b.2).

Key point: the extra turn is a new turn, so the "once per battlefield per turn" scoring limit resets (Core 470). Your opponent, whose turn got pushed back, gets nothing — holding only happens during the holder's own Beginning Phase (FAQ #8241). One caveat: you still need to control the battlefield on that extra turn's Beginning Phase to hold it.