Apple iCloud and Restoration (URGENT)?

Okay so I'm in quite the predicament.
I completely destroyed my iphone 6s, and got a replacement shipped to me as soon as possible because I pay monthly insurance on my phone,
However, my iCloud has not updated in 3 months because I was out of space and stupidly kept ignoring all the notifications, particularly because I did not want to buy more space.
When I got my new iphone today, it restored to the settings from August 2017, and here we're in October. I started a new business venture, and it is EXTREMELY important that I'm able to somehow recover all the texts and photos and settings that were on my iphone.
I did update the amount of icloud storage I have, and I still have the old iphone in my possession.
My question is, is there any way I could plug my busted iphone into my laptop and somehow transfer the information such as contacts, photos, etc. To my laptop and onto the new iphone?
I'm desperate. If that's not an option, is there anywhere I could take the phone where they can recover such information?

the screen on the broken iphone is so destroyed that the phone is completely unusable other than to maybe plug it into the computer. The screen has no functionality left whatsoever.

Any help is greatly appreciated. L

All data on iPhones is automatically encrypted. So even if you took your broken phone to a data recovery company and paid a fortune, they'd only recover meaningless digital drivel.

The only way you can sort this out is to connect your broken iPhone to iTunes on your host computer and then fully back it up. If it will not work in it's damaged condition then you'll have to pay to get that phone fixed sufficiently to allow the data back up to occur. Depending upon the level of damage that could be very expensive and need a specialist repairer, but if the data is that vital to your business then it's your only option.

Once that's done, you restore that back up to your new iPhone.

Learn from the experience and make sure that you always have a business disaster recovery plan. That may entail buying another new or used iPhone as a fall-back device, and consider using more options than just iCloud alone to back up your most important data. What if iCloud went down for any reason?