I lift heavy - particularly for my age & when I started (I started at 58 - if I'd started in my 20s I'd be lifting really heavy!) and when my gym ran Pump classes I'd do one a week or so. I also do HIIT classes, and metcon with my PT.
My HR does go up when I'm lifting heavy - by today's 4th working set (4 reps at 85 kilos) I was a bit out of breath. But I think it's anaerobic rather than aerobic.
The Pump instructor at my old gym used to say explicitly at the start of a class, that the weights in a pump class were not enough to build muscle. That they would work muscles, but not build them. Pump class is a version of aerobic exercise with added weights. The DOMS (if you get it - I didn't) is generally from muscles not being used to the repetition.
Whether other posters like it or not, there is a science to this. I'm not an exercise scientist, but my gym has a couple of trainers who have PhDs in the area! They advocate plyo work, metcon work, and heavy lifting. I'm not the only woman in my 60s at my gym lifting heavy, and almost all the women at my gym lift heavy, or are training for Hyrox, or bodybuilding.
My physiotherapist advises me that muscles like load, cartilage likes load - that's how they grow and stay working! Our bodies are amazingly adaptive - that's what "getting fit" is - a process of testing your body to its limit, resting, then your muscles adapt during that rest, so that the next time you push your limits, your body is more prepared. It's pretty magic.
But it took me 5 years of 2 - 3 times a week weight training to get to a 100 kilo deadlift, and a bodyweight (70 kilos) barbell back squat to proper depth. It's slow. And you don't test 1RM more than every 6 months or so. Today, for example, I did three sets of warm up deadlifts at 12 x 40 kg; 8 x 70 kg; then 5 working sets of 4 x 85 kg.
And @Ilostallthepens is right - a lot of women could lift more than they do. They don't have to if they don't want to, but I think it's a pity that women refuse to even contemplate lifting heavy. But I'm future proofing my body. Barring accidents, the way I train will keep me active & upright into my late 80s and 90s.