Mid-2012 Macbook Pro, Dual Harddrives - Catalina Update Slowing Down, Always Beachballing
You ran EntreCheck, but did you take any of the recommended actions based on what it found?
There's a lot to unpack here, but let's tackle it from a bird's eye perspective...
Beach balling
Beach-balling is the colloquial term to describe the spinning, multi-color icon when the system &quot;hangs.&quot;  This due to the system having to wait to execute the next command meaning that there isn't enough resources available for what's required.  From EntreCheck
System Load: 2.77 (1 min ago) 2.19 (5 min ago) 1.66 (15 min ago)
Nominal I/O speed: 0.64 MB/s
File system: 36.33 seconds
Write speed: 500 MB/s
Read speed: 519 MB/s

This means that your CPU is oversubscribed and is  taking too long to get data when it's requested.  Your main bottleneck here is your file system and (IMHO) this is due to your hard drive setup (see below).  However, with respect to system load and beach balling, if the system cannot get data quickly, the CPU has to wait, the longer the CPU has to wait, then subsequent tasks have to wait as well.
Drives:
disk0 - TOSHIBA MQ01ABD100 1.00 TB (Mechanical - 5400 RPM) 
Internal SATA 3 Gigabit Serial ATA

disk1 - Samsung SSD 840 EVO 250GB 250.06 GB (Solid State - TRIM: No) 
Internal SATA 6 Gigabit Serial ATA

You have your system on the faster SSD connected to the faster (SATA III) interface whereas your user data is on the slower HDD connected to the slower (SATA II) interface.  From this setup, you are literally making your CPU wait when user data must be accessed.
32 Bit Apps
Catalina doesn't support 32 bit apps so the fact that you're currently running 32 bit apps under Catalina says that you did an in-place upgrade of macOS.  In general, I'm not a fan of in place upgrades of any OS especially macOS.  Apple often makes (often radical) changes to things from one OS to another.  I have found that starting with a clean slate is usually the best course of action.  If you had issues prior to the upgrade, you will still have issues after the upgrade except they're possibly made worse by the differences in how things are done.
I suggest doing a clean install of Catalina or Mojave if you can't live without those 32 bit Apps.
Drive Layout
This is a confusing layout at best.  I think you wanted to segment your user data to the 1TB hard drive and leave the SSD for the system.  The problem with this is temporary files - that's usually stored on the system drive.  So, even in an ideal setup, you're still going to have that crossover where there seems to be duplicates on both drives.  The other issue, discussed earlier, is the disparity in transfer speeds; specifically the interfaces for each.  The primary is SATA III (6 Gbps) where as the secondary is SATA II (3Gpbs) - literally half the other.
Your best bet here is to avoid this complex setup and just go with a single drive setup.  A simple 1TB SSD can be had for less than $100 USD makes this a simple and easy fix.  Connecting it to the SATA III interface will ensure it gets the highest throughput.  Then use the slower drive on the slower interface as your &quot;self contained&quot; Time Machine backup drive.
The next option here would be to create a Fusion Drive out of the two installed drives.  While it's not as fast performance wise as a pure SSD, you will definitely see better performance because it will manage what data resides on the spinning hard drive and what resides on the SSD.  You will also have greater capacity - 1.25TB - with greater flexibility to make use of.
A third option is to get the 1TB SSD and use the existing 250GB SSD in a core storage volume and then use the 1TB HDD for backup.  You will just need an inexpensive USB to SATA adapter/enclosure.  This will give you a nice option for backups.
Time Machine
From EntreCheck:
Major Issues:
  Anything that appears on this list needs immediate attention. 
  No Time Machine backup - Time Machine backup not found.

There's no point in running EntreCheck and not following it's recommendations.  You've got a well bodged setup and nary a lifeboat in sight!  From unsupported and unsigned apps (per EntreCheck) an overly convoluted drive setup I'm surprised that a backup isn't enabled on a nearly decade old machine!  Even if everything was perfect in it's setup, it could still fail due to old age!
My recommendation is to get a Time Machine backup going immediately!  There are so many issues that get asked about here on Ask Different that can easily be fixed with a restoration from a  Time Machine backup.
While this is last on my list, it's actually the most important action you can take at this time.  Before attempting any fixes, you should tackle this first.