The problem with buying the thunderbolt 2 to thunderbolt 3 cable is that OP will pay $69 for a cable that he may use only once.
Better to take that money, throw in a little more, and buy a 1tb external USB3 drive.
Use the drive as "the medium" for the migration.
And afterwards, the OP will STILL HAVE the drive to use as a backup for the new MBP.
I would suggest a USB3.1 gen2 drive that is rated for 10GB transfers.
The Samsung t7 would do it.
Or, put together a drive by using:
- an "nvme" blade drive of your choice (many available)
and
- a USB3.1 gen2 enclosure (also many available)
Some of these just "snap together". Easy as pie.
Use disk utility to erase it to HFS+ (Mac OS extended with journaling enabled, GUID partition format)
FOR THE ACTUAL MIGRATION, I recommend creating a cloned backup by using either CarbonCopyCloner or SuperDuper.
BOTH of these apps are FREE to download and use for 30 days.
"Doing it my way" will cost you no money.
Important: for best results, you DO NOT WANT TO OPEN THE LID on the NEW MBP unless you have the backup nearby and ready to connect.
Connect the backup and open the lid for the very first time -- the new MPB will boot automatically to the setup assistant.
Begin setup. At the appropriate moment, setup assistant will ask if you wish to migrate from another Mac or drive. YES, you do.
"Aim" setup assistant at the backup drive, and give it time to "digest" everything.
This takes a while, so be patient.
Setup assistant will present you with a list of stuff to be migrated (apps, accounts, settings, data). IT'S UP TO YOU to select what you wish to migrate.
I'd just accept the default of "everything" and let it go.
Migration will take some time, so again, be patient.
When done, you should see the login screen as you did on the old MBP.
So... log in and "look around"...