Thunderbolt 2 cable for use with Migration Assistant

Good day, all

I just bought a 16" 2019 A2141 (OS Sonoma) and I would prefer to run the Migration Assistant by connecting my old 2014 15" MacBook (OS Catalina) by cable. You can tell I'm cheap as I've clung to my 2014 for so long. But it still does everything I need. I only updated to the 2019 because both speakers failed.

As you know, the 2019 has the USB C ports while the 2014 has the old Thunderbolt 2 and old usb 3 (5 gbps) ports.

Amazon has an C to Thunderbolt 2 adapter (https://www.amazon.com/gp/product/B01MQ26QIY/ref=ox_sc_act_title_1?smid=ATVPDKIKX0DER&psc=1) for $49 but the Thunderbolt port is female so I would need a cable to the old MacBook. Amazon sell a Thunderbolt 2 "data" cable but it's $80.

They also sell inexpensive display cables but most say they don't work for data transfer.

My question is: can I use the usb 3 port on the 2014 for Migration Assistant or simply in target mode? I tried once and the new Mac couldn't see the old one. Maybe I have the wrong usb C to usb B adapter or the usb B cable was data capable?

Thanks

Hugh