As I mentioned, I don't use Time Machine, nor do incremental backups. So, some of the questions I am going to ask are somewhat "basic".
OK, so Time Machine cleans up "older stuff" by itself, according to what you said: "When it fills up the backup drive, it clears up space by itself". Hence, that implies that except for your Downloads folder, there is nothing "unique" on your Time Machine backups that is not on your machine. Is that a valid statement?
Next, if you delete a document between incremental backups, does it get deleted from your Time Machine backup when the next incremental backup runs? (I understand about modifications to documents).
When you say "When we get a clean system, Migration Assistant asks if we want to migrate from the Time Machine backup", I get that whenever I do a clean, fresh installation of the Mac OS. (It actually says "Time Machine or other backup"). I assume that is what you mean by that. But does that happen when you do a Mac OS upgrade "in place"? Given that the only "in place" OS upgrades I do are within the same version of the Mac OS (for example, I upgraded "in place" from OS 10.14.2 to OS 10.14.3 via the Combo Updater, but I don't remember getting that message), not sure what happens when one upgrades in place say from the last version of High Sierra, OS 10.13.6, to whatever version of Mojave.
For #3, the assumption I made was that you would start to use either SD or CCC for your backups, and that there was nothing unique on your current Time Machine backups that you need. The process would involve 1) doing some more "intense" manual cleanup, 2) run Onyx, and 3) use a more advanced tool like Tech Tool Pro. Assuming that gives you a complete clean system, you would then use SD or CCC to make a full backup. That backup, obviously, would be clean also. From there, it becomes an issue of whether you need to do incremental backups or not. As I mentioned, for my needs, I don't need to do that, and my weekly backup completely replaces the prior one. So, when I do my disk cleanup/maintenance/repair, and backup tasks tomorrow, SD will replace the backup I did last Saturday with a new one.
Again, though, I am meticulous (and dedicated) about keeping my systems "lean, mean, and clean" between backups. If I were to do incremental backups, I of course would do the same.
I don't know what kjams is (seems to be something to do with karaoke:
https://karaoke.kjams.com/). When you receive an EMail that you do not need at all, do you delete it right away (that is what I do), or do you first save it in one of your folders? If you delete it right away, it does not get permanently removed unless you take additional steps. Those additional steps (or step) depend upon the EMail program you use. I use Thunderbird, and it is a simple, one step process to do that.
If you use SD or CCC in addition to Time Machine, you do not need to store that backup off site. You just need a separate external drive that you can keep somewhere near your machine. I actually have 2 external devices (each of them house Samsung SSDs) that I use for my backups. The cases are nice, slim Orico enclosures that take up very little space, and I connect them via USB to either or my Macs. I even take one with me whenever we travel someplace (I take my MacBook Air with us).
As for Tech Tool Pro, this link has a good description as to what you can use it for:
Techtool Pro is Mac utility software for maintaining and troubleshooting your Mac, including drive repair, RAM testing, and more.
www.micromat.com
Given that I have SSDs inside both of my Macs (and my external drives are SSDs), I don't run Volume and File Optimizations (that's a no-no with SSDs). The Surface Scan feature is useful for detecting issues with a drive (internal or external, SSD or traditional HDD), but I only run it about once a month or so. The tasks I run every week with Tech Tool Pro (after running Onyx) are:
Memory Test
SMART Check
Partition Map
Volume Structures
Video Memory
Sensors Test
File Structures
Fans Test
Battery Check (only for my MacBook Air; not for my Mac Min i)
Volume Rebuild
Again, by doing a lot of disk cleanup on my own between my Saturday backups, then running Onyx, Tech Tool Pro, and SD (in that order) on Saturdays, I rarely, if ever, have issues.
Finally, for your Downloads folder, how "clean" is it? Are there any items in it that you no longer need?