Aye - the reality is that whilst weightlifting (ignoring here Metcon or crossfit-style cardio workouts) causes heart rate rises, this is due to thoracic pressure rather than aerobic fitness pressure.
It’s hard to quantify any exercise that isn’t cardiovascular in nature using heart rate data. I’ve heard of including lifting etc in CTL - but the problem with this is that it impacts upon your form (aka your tiredness and capacity to conduct workouts). Whilst lifting will impact your muscular ability to complete workouts, it will have little to no bearing on how well prepared your cardiovascular system is for conducting difficult workouts, races e.t.c.
Probably best to allow all variable sport types to be given a custom factor but my default would be only cycling, runnning, crosstraining, ski touring, xc skiing e.t.c.