I've never owned either one but nonetheless flirted with the idea of getting the Pana 12-35mm f2.8 or Oly 12-40mm f2.8.
However, I've never judged (for micro four thirds) f2.8 to be sufficiently wide enough for low-light shooting without flash with moving subjects; and if my dimly-lit subjects aren't moving, then a slower, stabilized kit lens or, of course, a prime would suffice (assuming I haven't had too much coffee).
Hmmmm, you seem to have divided low-light subjects into two distinct categories: (1) moving subjects for which f/2.8 is not fast enough; and (2) non-moving subjects for which your P12-60 or P12-32 are fast enough. I don't think it is that simple.
I've clustered things that way because, well, that's how I tend to shoot. Help me understand what I'm missing
For people, I usually need 1/50sec if I'm posing them, 1/80sec for general candids, and 1/125sec or faster if playing, opening presents, etc., and, of course, 1/250s and faster for sports. If I'm not using flash, I usually need f1.8 or faster to keep ISOs in the most comfortable part of my IQ comfort zone (<=3200, although as I use DxO and shoot RAW I'm willing to go to 12800 or even 25600 if that's what it takes). Thus, in general, f2.8 is still extremely marginal for me indoors unless I'm using flash or have nearby windows during daytime. And under those circumstances, I could likely shoot the same scenes with my f3.5-5.6 kit lens.
For indoor "stuff", with my G95 and 12-60mm, 12-32, or 9-18mm, I'm usually confident hand-holding down to 1/6s, often 1/3s is doable for me, and sometimes 1/2s or even a full sec is do-able, depending on whether I can brace and how much I'm being rushed by my family to stop being such an insufferable slow poke photographer. Under all but the worst lighting, such as the interiors of amusement park rides, I can typically get by with a kit lens while keeping ISO within my IQ comfort zone.
Here are two examples I took of a Harry Potter theme ride at Universal Studios with my least trustworthy combination (in terms of dual IS not really giving me a whole lot) GX85 and 12-32mm. I'm fairly sure I could have shot these a half a stop to a full stop slower on my current G95 body.

GX85 + Pana 12-32mm @ 1/3 sec, f3.5, ISO2500, RAW (DxO)

GX85 + Pana 12-32mm @ 1/3 sec, f3.5, ISO320, RAW (DxO)
If you are indoors shooting at 32mm, f/2.8 can be a significant advantage over f/5.6. I have often gone out with just the 12-35, expecting that the range would be sufficient and f/2.8 would be helpful (as compared to the 12-100) and sufficient. For me, there was enough of a use case for the 12-35 to keep it after I got the 12-100.
Indoors, I'm most commonly shooting medium to wide focal lengths rather than tele, so I feel I'm down around 1 stop to the f2.8 lenses when using my 12-60mm kit lens.
Therefore, for a mainly good light (but occasionally dusty/wet/muddy conditions) shooter, the pros of these f2.8 lenses vs. say, a weather sealed 12-60mm Pana f3.5-5.6 kit lens, seems mainly down to slightly better edge and corner resolution, slightly better background blur (within the overlapping lengths), better flare and CA resistance, and better build quality/pro feels when you handle it.
Is that right?
I haven't used the P12-60, but it seems to be highly praised for punching above its cost. If 3.5-5.6 works for you, I'm not able to claim that the 12-35 is better in the respects that you list. Except it is obviously capable of somewhat narrower depth of field. Build quality is good, but not as stunning as Oly pro lenses.
Does this account for the secret "gorgeous rendering magic pixie dust" sprinkled over these lenses when they leave the factory and you have to just try it to discover it's totally worth giving up the added 35-60 (or 40-60) focal length?
I do like images from this lens, but perhaps that is just confirmation bias.
Sorry, it sounds like you are doing fine with the kit you have!
Well, I'm afraid that may be the crux of my problem. I may need to become more dissatisfied somehow.
Thanks for commenting!