OP:
I WOULD NOT BUY the thunderbolt2 to thunderbolt3 adapter, because
I don't think it's going to work with a thunderbolt1 device.
See this page:
https://www.apple.com/shop/product/MMEL2AM/A/thunderbolt-3-usb-c-to-thunderbolt-2-adapter
It mentions thunderbolt2 ONLY, with
NO MENTION of thunderbolt1.
It -might- be possible, but I wouldn't buy it until I had read other user reports of success.
Also, if your thunderbolt1 drive runs on "bus power" it won't work with this adapter, because it doesn't provide any power.
OK, having said that...
Is the thunderbolt drive you have now "openable"?
In other words, is it accessible so you could take the SSD
OUT OF the enclosure?
If you can, you can put it into a USB3/SATA 2.5" enclosure, and connect it right to the 2018 Mini.
This way, you can use it for migration, and then re-purpose it afterwards.
BUT -- if you CAN'T easily open the drive, there are "other ways" to get at the data as well.
Do you happen to have a spare hard drive around?
Can be an SSD, could be a platter-based HDD, ANYTHING will do.
Only requirements are that it has to be USB, and has to be large enough to hold the contents of the thunderbolt1 SSD.
If you have something like this, you could do the following:
a. Download CarbonCopyCloner (FREE to download and use for 30 days)
b. Clone the contents of the thunderbolt1 SSD to the USB drive
c. Now connect the USB drive to the 2018 Mini and "migrate from there".
Re your other data:
The NAS and other external drives can work with the 2018 Mini as well as they work with the old one.
I'd just "leave them be" for now, and worry about migrating that data in the future.
Your first concern will be to get your apps/accounts/mail (etc.) from the thunderbolt1 SSD to the new Mini, and get your user account set up so you don't have permissions problems later on.
THE WORST THING YOU CAN DO is to boot the new Mini right away, create a "new" user account (usually with the same username and password as you used on the old one), and then try to "migrate" from there. It can lead to all kinds of permissions problems.
I'm not saying that one cannot do this.
But if one does, one had better understand HOW to work around the permissions issues.