I think that so that you don't keep waiting, you should contact the hiring manager directly, more than a month is a long waiting time, and more so for a company like Target that is always hiring staff. When communicating with the hiring manager, you can be totally honest and tell them that you have been waiting for a response from their company and that you would be excited to work for them, but in case there is no possibility, you would like to know to look for new options.

Target registration for an ALB target shouldn't take long. It sounds like perhaps the NLB just can't reach the ALB. A quick thing to check first would be that the target port number in the NLB's target group matches the listener port on the ALB, and that the security group attached to the ALB allows inbound traffic to that port from the NLB. If you attached a security group to the NLB, it also has to permit outbound traffic towards the ALB and the correct port number, but since all outbound traffic is permitted by default in newly created security groups, this is less likely to be causing the issue.

I would wait until maybe monday to give a call, sometimes it takes us a while to look at the interviews. Good luck!