Skipped the build, bought a house that already had a legal ADU

An open permit and an unpermitted unit are two different problems, and you had the better of the two. Open permit means the city already agreed the use was allowed and the plans passed review, so you were buying a punch list. An unpermitted conversion means the use itself may never have been approved for that lot, and in that case the corrections aren't a punch list, they're an application.

One thing to know for anyone reading: how permit records are kept and what a seller has to disclose about them varies by state and by city, and a few jurisdictions make you request the file in person. Ask the building department for the full permit history on the parcel in writing, and read what the final inspection card actually says. Whether an unsigned final creates a problem for you specifically is a question for a local attorney, since it turns on local code enforcement practice.

The number I'd want tested is the $1,450. What does a 410 square foot studio with a kitchenette rent for in your submarket if you had to re-lease it in a slow February? If the answer is $1,150, your out of pocket goes from $1,240 to $1,540 and the deal still works because you'd be paying rent somewhere anyway. If the answer is $900, it's a different conversation. Do you know what the comps actually are, or is $1,450 what the first applicant agreed to?

Running your figures as stated. $1,450 gross, call it 8% vacancy and turnover reserve, $116, and the marginal utilities and maintenance the studio adds, maybe $150 if it's on your meters. That's roughly $1,184 net against a $2,690 payment. So you're housed for about $1,506 all in, plus whatever the main house costs you in repairs that you'd now be paying as an owner instead of a renter. What's your prior rent? That's the only comparison that tells you if this worked, and you didn't post it.

kestrel, worth knowing for your refinance later: an appraiser looking at that property will treat a legal permitted second unit very differently from a studio with a kitchenette that reads as bonus space. Get a copy of the signed final and the certificate of completion into your file now while you can still get the city on the phone about it. When you go to pull equity in four years, the person underwriting it will want documentary proof that the unit is legal, and "the seller said so in the listing" is not that.

Basic question since I'm still learning the vocabulary here. Is a kitchenette enough to make something an ADU, or does it need a full kitchen? I've seen both words used and I can't tell if it's a legal distinction or just a size thing.

The service gap in what you just described is enormous. Nobody sells "pull the permit history and tell me what's open on this parcel" as a product to buyers under contract, and you needed it ten days before closing. Filing that away.

Managing side of this: your lease needs to say who parks where, and it needs to say it in the lease, not in a conversation on move-in day. Attached garage conversion means the driveway is now shared and the studio tenant probably has no dedicated spot. Second thing, if the studio is on your electric meter you will eventually have a tenant running a space heater in December and you'll be paying for it. Cheap fix is a utility allowance written into the rent with a cap. Expensive fix is submetering after the fact.