Can removing the internal hard drive help me recover my data?
Yes indeed. Here is a kit that would get you a new drive and a sled to do data recovery on the old drive.

https://eshop.macsales.com/shop/ssd/owc/macbook-pro-retina-display/2013-2014-2015

If you just need the sled, that’s cheaper. Or you could pay a recovery service to do all the work.

https://drivesaversdatarecovery.com/

For DIY recovery, Data Rescue is amazing and great value for what it does.

https://www.prosofteng.com/