First, if you plan to upgrade to the next Mac OS, your current 32 bit applications will no longer work. Hence, you'll need to either upgrade them (assuming upgrades are available), or find a 64 bit replacement program. Myself, I have 2 such 32 bit applications that will not work when I upgrade: Quicken 2007, and Magic Number Machine (a calculator). I really like Quicken 2007 (it reminds me of reliable old COBOL software!), but I also have Quicken 2017, which is 64 bit. Have not found a suitable replacement yet for Magic Number Machine.
Secondly, your concerns about "problematic "stuff" on your Time Machine backups is a valid one. If you were (after "cleansing" your current setup) to use another backup program like SuperDuper! or Carbon Copy Cloner, either of them will capture EVERYTHING on your current system. But if you have anything on your Time Machine backups that are no longer on your Mac, and you absolutely need any of that, well, that's a more complicated issue. So, the question is whether or not any of your Time Machine backups contain anything that is not on your current machine that you absolutely need? Only you, of course, can answer that.
Assuming there is nothing "additional" on any of your Time Machine backups that you need, there are definitely some strategies you can pursue. I know I am going to repeat myself here (as other folks will note also), but the issue you raise is just one of the reasons why I continually state that I keep my Macs "lean, mean, and clean", and I make a concentrated effort to do that on a continuing basis. The analogy I use with automobiles is again relevant here. One of the automobiles we own is a Toyota Camry (actually the second one we have owned). It is certainly one of the most reliable cars in the world (as are most Toyota and Honda models), but it is still necessary to take care of it. I myself do some simpler maintenance on it (along with our other vehicle), and of course I take it in for regular, scheduled maintenance. Well, Macs are no different. Unfortunately, the majority of folks neglect to do that (just like the majority of folks neglect to take care of their automobiles).
In any event, given that you have a backup already (which is good), here is one approach:
- You will need to use some of your own efforts (explained below).
- Gather up all the software you will need. You already have 2 excellent products in Onyx and AppCleaner. It would be best if you invest in a more robust disk cleanup/maintenance/repair program to work in conjunction with Onyx. Given that you use Mojave, the "best" one is Tech Tool Pro (I use it, along with Onyx and SuperDuper!), It costs $100, but sometimes it is on sale for as low as $40 (typically in the fall).
- You'll need to obtain either SuperDuper! (SD) or Carbon Copy Cloner (CCC), and the latest version of the full installation file for Mojave. Besides price, the main difference between SD and CCC is that one can also backup the (hidden) Recovery HD partition with CCC. For me, though, that is not a detriment, as 1) that partition gets re-created with a new installation of the Mac OS, and 2) one can install it anyway.
Let me know if you want to pursue this, and I'll provide a more detailed, step-by-step plan. Two things you can do right away are 1) permanently remove deleted EMails with your EMail program, and 2) whenever you download a newer version of a program, get rid of the prior version (assuming you keep it around). That saves disk space, along with making things less cluttered. Also, an obvious place to look for "unneeded" files is your Downloads folder.