I’ll up your pedantry with even more pedantry, colloquially “bought a house” is understood to mean “closed a deal on a house with financing” - “bought a house outright” would be for a full cash purchase.

I don’t mind unnecessary pedantry where appropriate, but you’re incorrect in this context.

And, technically speaking, when you buy a house (mortgage or not) you become the owner of that house - you’re just also receiving a loan with your house as collateral. So, if you fully paid off your house and then applied for a loan to start a business would you consider your house no longer owned by you?

If we really dig down here your pedantry about buying a house becomes quite meaningless because the loan using your house as collateral doesn’t mean you’re any less an owner of your house - you own it, fully and completely, you just also have an outrageously large loan using it as collateral (granted it’s a pretty special loan for a number of good social reasons).

It is extremely good to acknowledge how much that loan interest rate is effectively increasing the price of your house though, far too few people realize how much actual money they end up paying.