What kind of lens is good for street photography using a mirrorless camera?

Remove the lens, attach the old lens and see if you get the same issue, if yes, then you have an issue with the base, and will need to be take to a repairman. If no issues, then the new lens is having issues. Since its new, I assume to will have a warranty.

Welcome to the club of lens droppers entry only requires that you drop and break lenses its an expensive club to join
I found my entry fee to be to high for continued membership once was enough
cheaper to buy another lens due to internal damage repair costs
Only way for you to find out is to get a repair quote as elements may be out of alignment
Good luck

maybe the sensor is faulty? possibly the lens is not very good? If it is producing bad results something may be amiss.
How does it work with another lens... if the result is the same then the issue is in the body's functionality.
You have tried adjusting the various settings to no avail so it may be a hardware fault.

Seee other response, I think that unles a change of lens brings a different result could well be a hardware fault

Here is the manual. For future reference, most companies host manuals on their support site.

https://docs.sony.com/release/ILCE-5100_Help_Guide_EN.pdf

If you're in the US, 1-877-865-7669

If you're not in the US, point your web browser at Welcome to Product Support Get the help you need then select your country at the top and go from there.

did you view this video on youtube, about how to use the apps? Time Lapse Sony PlayMemories Camera App

What kind would you like to get? Cameras vary widely in size, weight, features, capabilities, ease-of-learning, ease-of-use, and, of course, cost. The best digital camera for one person is very unlikely to be the best camera for another person.

Visit your local library or bookstore. There are plenty of introductory books that discuss camera types and the trade-offs they offer.