Your old adapter is Mini DisplayPort to VGA, not Thunderbolt to VGA. It works with your 2013 laptop because computer Thunderbolt/2 ports are compatible with Mini DisplayPort. The Thunderbolt 3 adapter is not.
About the Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter - Apple Support
"This adapter is not compatible with displays that use DisplayPort or Mini DisplayPort, such as the Apple LED Cinema Display. Thunderbolt and Thunderbolt 2 are not the same as Mini DisplayPort, though the ports have the same shape."
You need a USB-C to VGA adapter, such as:
https://www.startech.com/audio-video-products/cdp2vga
"Thunderbolt 3 port compatible"