Thank you for taking the time to answer my questions, Old Toad. To your thoughts:
#1 - unless you have as much space on your new Mac or more you can't use Migration Assistant to migrate your data to the new Mac.
Migration Assistant will, in fact, let me copy data to a smaller drive - just not all of it (as you noted to an extent in #2 of your response).
I was able to use the "twisties" (little arrows indicating a section that can be opened) to select parts of my data, including my settings, which fit comfortably on the new, smaller drive. Once all the sizes were calculated, I clicked on a twistie to reveal it's sub-sections. Then, selecting/deselecting sections gave me the new sizes. Once I had everything I could get that would fit, Migration Assistant allowed me to continue and successfully install the data I had selected.
#2 - Y0u can connect the eternal drive to the old Mac and copy the contents of the Documents, Music, Photos and Movies folders to the external drive. Note: make sure you can open the libraries from the external drive before deleting from the internal boot drive. ...
I got the new Mac Mini because my older MacBook Pro 2017 had died - ie, it won't even power on. The 2017 has a soldered-on hard drive - which can't be removed and placed into an enclosure for data retrieval. (At least not at my level of proficiency in hardware repair.)
I did, however, have a full Time Machine backup. Again, Time Machine actually has an option to "Restore ... to ..." a different location, including external drives. However, that option is not currently working on Sequoia 15.5. I did report this in a feedback to Apple.
Instead, I used the "Copy" command, within Time Machine, to copy the data that wouldn't fit on the Mac Mini into a large external drive I had formatted for the purpose of holding the MacBook Pro's extra data. That required slightly different steps, but worked great! Now, I have all the data from the MacBook Pro's much larger drive stored nicely on an external that I can even add to my new Mac Mini's Time Machine backups.
And, as far as the comment:
In the future always get the same or more storage than you had on the old Mac.
I hadn't planned and budgeted for a new computer at this time, so coming up with the cost of a replacement at all - let alone an additional $400 to push the Mac Mini's 256 GB to a full 1 TB - wasn't an option. I had to make due with what I can currently afford while still budgeting for a new high-end MBP within the next year or two.