Heya @ljkuipers (Laura) and welcome to Kinsta Community!
You could just enable the HTTPS option for your local site from DevKinsta → Sites → Site name in question (Site info page)
and if you still get the unsafe/unsecured warning ( “Your connection is not private” / “NET::ERR_CERT_INVALID” for that local site (with https:// URL of your local site), please check if you’re accessing it with Chrome browser ?
If that so, please try with different browser, such as FireFox and see if it’s opening just fine there.
I also have this issue with Chrome browser (on the current updated versions, but didn’t have this issue before on the previous version) as I mentioned in the other thread here. Please see if that’s the same case as you’re experiencing and if accessing with different browser (FireFox) will help.
Regards,
Agus