Most services that I've seen mostly have automated verification processes where if you meet the requirements set by default, your verification will be done pretty quickly, right after the application is processed, but if there are mistakes or problems like no clear documents or mismatching information, then the case is handled manually which takes more time.
When a case is handled manually, it depends on how many existing requests a platform has and your case will be handled according to that, most of the time it's on a first come first served basis so you will have to wait until the previous applications are cleared.
This is my experience as well, as long as you submit your documents and the scans have a good quality you can get your verification done very quickly, but if you made a mistake or the documents are not as clear they should be or something like that then the manual verification will take place instead and this could take way more time, because as we know the customer support of most casinos is overwhelmed with all kind of requests, and depending on the standing of your account you may not be prioritized at all.