Best way to transition from /24 to /16 without dropping communication

I'm trying to provide some advice on a project to expand a network subnet. The issue is there are ~200 devices with all static IPs/Subnets that report back to a server, 192.168.1.1. Each device requires a local visit and an SSH session to configure the network settings.

---

Original Server Network Address

IP: 192.168.1.1

Sub: 255.255.255.0

---

New Server Network Address

IP: 192.168.1.1

Sub: 255.255.0.0

---

If I first expand the subnet on the server, will I still be able to communicate to each existing field device as I go to them and expand their subnet?

Will broadcast messages from 192.168.1.2/24 still be seen by 192.168.1.1/16?

I understand that 172.16.X.X SHOULD be used for a Class B network. This was poor network planning from the start ~10 years ago.