DIAGNOSIS The printer's wireless module is probably still trying to connect to your old network's SSID (name). It won't broadcast itself for setup until it's explicitly told to look for a new network or reset.
FIX The easiest way is to connect it temporarily via USB to a computer. Use the Brother software (like ControlCenter) to access the settings and run the wireless setup wizard from there. If you don't have the software, you can do it from the panel. Press the 'Wi-Fi' button on the front. Use the arrow keys to navigate to 'Network' > 'WLAN' > 'Setup Wizard'. Let it search for your new network and enter the password.
IF THAT DIDN'T WORK You may need to reset the network settings. On the panel, go to Network > Network Reset. Confirm. This will wipe all network info. Then immediately run the Wireless Setup Wizard again as if it were brand new.
HEADS UP If your new router is broadcasting on Wi-Fi 6 (802.11ax) only or using WPA3-only security, this older printer might not be compatible. You may need to enable a legacy mode (like 802.11n/g) or WPA2 on your router's settings for it to connect.