I think the problem in what you did for an assessment is that you use total volume of multiple sets. Doing that, you could lift more by simply doing more sets of whatever rep range, or even do enough single reps to eventually show improvement. What you are reporting is simply comparative training volumes.
I think to more accurately assess strength gains, you need to compare equal situations. To do that, I think you need to assess what you can do in comparative single sets to failure.
So, if four months ago, you could do a squat for a max of 6 reps with, say 200 pounds, and now you can do a max of 6 reps with 250 pounds, then you got stronger. Same, I think, if you now do 12 reps with 200 pounds, versus the 6 reps you could previously do. But I don't think you can (easily, at least) compare strength based on total volume the way you did. Of course, I could easily be wrong. But it shows movement in the right direction, I think.
So, just look back at your training log to see what you could do for one set to failure, and then try that now as a comparison. You should be able to use more weight, or do more reps with the same weight.
Of course, I think there is also the different matter of strength as illustrated in increases in a set of 6 or 8 reps max versus that shown in an increase in 1 RM. Different muscle properties.
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