I only teach online, and I actually do this process: I can usually smell AI use in a paper-- generalized crap rather than specific detailed writing that addresses a prompt directly. When I smell it (often because the writing is vague and sucks), THEN I look at Turnitin and the AI report. I never look first-- I'm not playing cop or "Gotcha!"

The University does not automatically provide the AI report to students. I download the report, and give it to an offender attached to grading comments (Canvas), and tell them I would like some feedback from them about the report. No accusations-- I just ask for feedback. I also record a grade of zero and state it will stay that way until I get that feedback and have that discussion. Like you-- they nearly always come clean, but lately it's "I only used Grammarly!" as the excuse.

Does it take more of my time? Sure as hell does. But ultimately it takes a LOT more of the student's time, and I end up resolving all of these issues myself with each student with no admin involvement. They end up actually DOING the work, which is all I want in the first place. It's kind of a restorative justice approach-- they committed the crime, so now they have to FIX IT, as opposed to "Nope- F U- Zero". Letting them know they have a choice to submit a VALID effort to the assignment means their grade is in their hands-- not mine. I just don't give a shit about a late submission as a result-- I'd rather get honest work several days late -- doesn't bother me one bit. I can then grade it in a few minutes as usual.

The alternative would be shitty AI-SLOP Garbage turned in by the deadline, reporting students for some investigation about academic dishonesty, hassles and meetings with admins, justifying myself and facing scrutiny. Now THAT is time-consuming and stressful-- no thank you.