Good day folks. I apologize in advance for my lack of knowledge on such a basic subject, hence why I post in the "beginners" section and not the "repair" one. Bare with us, as my terminology may be all over the place

TL;DR: I'd like to ask for a few pointers on how I should go about doing some basic tests on a bunch of op-amps and comparators without a scope or other advanced tools, since I don't have those

I do have the trusty multimeter and bench supply at my disposal

Of course, this is just enough to confirm they're not obviously faulty and may not fully reveal the more "advanced" parameters which may be out of whack - I'm aware of that.
The reason I need to do this is because I'm faced with a faulty Legrand UPS I wrote about
here, but got no replies so far - understandably, it's a very complex issue and that's a very long post, so fair enough

In an attempt to narrow the issue down, I suspect I'm dealing with a faulty op-amp/comparator/schmitt trigger somewhere, so I need some help with my test methodology, since it doesn't seem to be working the way I initially expected.
Based on
some resources I found, which don't always seem to agree, the way I did it so far was by removing the comparator from the board (obviously) and then connecting the Inverting input to GND and the N/I input to VCC via 10k resistors (Fig.1 in the crude schematic I drew). I'd power it with anywhere from 5v to 12v from my bench supply and measure the output: in this config, it should read close to VCC (yes yes, I'm aware it will not go all the way up TO the rail, but it's still a good indication it at least did something and it's not stuck at GND).
Next, I'd reverse the inputs like in Fig.2 and this is where the confusion began: since the N/I input is now lower than the Inverting input, I'm expecting the output to also swing LOW (to GND).....but it doesn't. Again, I'm not completely clueless: I understand part of the problem, but not all of it: there's push-pull op-amps/comparators and there's open-collector op-amps/comparators. Open-collector ones SINK current, like an NPN (which is what the "output" actually is), so without a pull-up resistor to VCC, the output pin cannot possibly read any voltage. The LM393 is like this and I experimented with it to confirm - fair enough, this part I get.
Then there's the Push-pull type: these actually seemed to be even more simple to understand. Ironically, I was having trouble figuring out the open-collector kind and figuring out why the hell my output was always stuck LOW (drove me nuts !), but it turns out push-pulls are tricky too. See, I THOUGHT that since they can both sink AND source current, the output would read high/low as I flipped the inputs between VCC and GND as described above.....which doesn't always happen though. Some do and some don't.
An example of one that DOES is the
TLC I played around with a while ago: ground the Inverting input and pull the N/I input to VCC and the output goes high. Flip the inputs around, it goes low - simple.
Today, I thought I could use the same setup to "test" some of the op-amps on the UPS board and this is where I got confused: it's mostly
TL074c op-amps on it and no matter what I try, the outputs are always stuck HIGH, close to VCC. First off, am I right to assume the TL074C is even a push-pull jobbie ? The schematic shows one transistor pulling up to VCC and another pulling down to GND, sooooooooo.....

I then tried another suggestion and connected the op-amp in "voltage-follower" mode: Inverting input tied straight to the output and used the 2 10k resistors on the N/I input as a resistor divider to get half of VCC. This worked and the output pin now showed half VCC as well, so can we assume the op-amp is "functional" just based on that ?
I distinctly remember I had the same exact dilemma a while ago with some
LM833s where the same behavior occurs (output always stuck high) and people pitched it and tried explaining why my circuit didn't work, but we never actually got to the root of the issue and whether this simple test CAN be performed on it in the first place.
Thanks for any suggestions.