I want to thank everyone who offered help.
Frankly, I'm surprised I have any hair left.
What a pain-in-the-patoot "migrating" is using 2 Mac Minis with just 1 (count 'em: one!) monitor-keyboard-mouse (MKM) set.
Round 1 nearly caused me to jump out a window.
I tried using an Ethernet connection but learned a "migration" could take...days. So I thought a Thunderbolt cable might speed things up (and ordering one calm me down!). So I went on Amazon to obtain it. 'Twas unpleasantly surprised by the price.
When if finally arrived, Round 2 commenced.
I set up the old Mac Mini (2018) for migration, then the new 2024 version.
The new one suggested I update it to the most-current OS...to match the other.
Hmmm. Was 2018 up-to-date?
To check, I unplugged/replugged MKM.
Ah, it did have the latest OS version.
So back to check the 2024 Mac Mini.
I reconnected it via MKM...only to find a displayed Migration panel. Oy! How could I update the OS on it with that panel blocking access to the desktop? I keep blindly trying things. "Something" finally worked, giving me access to the new Mac Mini as if I were setting it up as-is, no Migration involved.
NOTE: while not a total technotard, I suspect I am more of a Luddite that you all. Not that I'd put my PC in a garbage bin if a techie suggested I "trash" something. (<:) Still, much of what transpired seemed like magic to my befuddled self. Too much "voodoo," really.
For example, when attempting to update the new Mac Mini's OS, the process bar (?) kept saying the estimated time for it to be installed was 30 minutes. Fine. So I kept staring and staring at it. No change in the "time remaining."
Grrrr!
Frustrated, I got up to grab some juice and walk off tension. Coming back 5 minutes later, the "estimated time remaining: 30 minutes" alert was gone. The new OS had fully installed, yet hadn't taken a half-hour.
What?
Why didn't the alert's time decrease as, you know, time went by? Why didn't at least graphic "bar" depict the passage of time?
I began to fear that I'd have to offer a chicken (or at least some chicken McNuggets) to appease the fickle Gods of Cyberia.
In any case, now that both computers were on equal OS footing, I hooked the MKM to the new one, opened its Migration Assistant, and greenlighted the process.
I then did the same on the old one.
If memory serves, 2018 indicated that I needed check off items to be migrated from it. I began to feel like a rookie Homeland Security Agent.
I think a number appeared, too. Things got fuzzy, so I'm not sure of exact sequences.
I selected what I wanted transferred to the Mac Mini 2024 and clicked a button.
And waited.
And waited.
Like I had during the OS update on the new machine.
Nothing changed. A "spiral of doom" graphic kept spinning and spinning and spinning. Like my head.
Frustrated yet again, I cursed the ghost of Chuck Babbage and unplugged the MKM from 2018. Replugging same into 2024...mirabile dictu! Staring me in the face was the same number on 2018 and a query asking me if I was ready to commence the migration. There was even a displayed button to click to do so.
Why hadn't 2018 told me that I had to go back to 2024 to finalize the process and "launch the cow" a la Monty Python?
When the Thunderbolted migration began, I think it took all of 3 minutes to complete!
Meanwhile, the whole process seemed like it took years off my life.
(For those who wisely suggested that I back things up: I'm Señor Overkillo when it comes to that. I use 2 external SSDs, 2 OG electro-mechanical drives, and Dropbox to b/u sundry things. I also backup the whole shebang using both Time Machine and BackBlaze.)
Whew! Hopefully I won't have to enter the Gates of Data Migration Doom for another 5-7 years. When I do, I will prolly ask you all for advice again, since I'm sure things techno will have gone from horse-and-buggyness to Muskian rocketry again...leaving me feeling like a pilgrim crawling to Mac Mini Mecca (if physical computers even exist then) on an empty stomach.

In the meantime, and again: thank you all for your suggestions. Yuda best!
Hasta Luigi!
~Robert