Official designer designed a logo for my lab but it turns out that it's just a copy from somewhere else, should I report it to the university?
I'm not sure if it is a violation of academic integrity or not cause it's not a research project

It is a violation of academic integrity.

Even I can't find any information about when this page is posted online

The Internet Archive shows the image existed on that page 26 July 2018.  Furthermore, it's advertised for sale:
https://stock.adobe.com/au/189585864?as_campaign=TinEye&amp;as_content=tineye_match&amp;epi1=189585864&amp;tduid=4956906e07434ca59f9d78b2979d22da&amp;as_channel=affiliate&amp;as_campclass=redirect&amp;as_source=arvato

should I report it to the university?

If you have used the logo, perhaps on a website, you should report this to university counsel.  They should figure out what to do to prevent litigation.
Of course it is possible the &quot;graphic designer&quot; purchased a license and then claimed the image was original work.  But it is more likely they did not purchase a license.
In a university context, you should have no tolerance for plagiarism by staff.