Spinning

I'm not spinning anymore (stationary bike at home now, in Winter, but it's not strictly a spin bike). I did spin classes twice a week before the pandemic, and had done for . . . years. Once I started calorie counting (2015), I used my Polar heart rate monitor calorie estimate, then my Garmin Vivoactive 3 calorie estimate (indoor cycling setting for the latter).

If the spin bikes at my class had had an average watts readout, it probably would've been more accurate to use that plus a standard calorie conversion formula for biking watts. I say "probably" because there's a question about whether gym bikes' calibration is reasonable, but if it is, that "probably" changes to "definitely". My gym's bikes didn't have a watts readout, so it wasn't relevant.

I do other exercise (indoor rowing) that does have a reasonable watts readout. Based on the RPE from doing that, and a comparison to the calorie estimates that machine provided, the Polar/Garmin estimates didn't seem crazy for the spinning, so I figured they were close enough for gubmint work, y'know?

The estimates were lower than MFP's stationary biking estimates (which are problematic in various ways), and my general rule is that when I'm not sure, I use the lowest generally plausible exercise calorie estimate if there's not an authoritative one.

On top of that, the workouts were only maybe 20%ish of my TDEE on spin days, and a smaller percent of my total calorie expenditure for the week, so the error factor was unlikely to arithmetically problematic.

It worked out fine, as a practical matter - I both lost and maintained pretty predictably using those estimates, FWIW. That may be a squishier way of thinking about it than some people would prefer, but it worked for me. 🤷‍♀️

Heart rate is not particularly good basis for estimates for cardio where your HR will be very variable - those estimates are massively affected by your fitness levels and how quickly you recover from the higher intensity bursts.
Steady state cycling (or other cardio) can certainly be reasonable enough for purpose though.

If your spinning bike displays power (in watts) it can give you a very accurate net calorie estimate (it will be slightly low if there are significant standing cycling elements to your session).
I wouldn't worry about the calibration issue reported by @AnnPT77 above, power meters are very simple and robust technology. Some bikes do however deliberately use a formula to exaggerate calories but you can check by multiplying your average watts per hour by 3.6

Methods based on displayed speed or distance (including the outdoor cycling estimates in the database here) shouldn’t be used for spinning or indoor cycling as you aren't actually moving anywhere and the speed/distance shown on the bike doesn't bear much relation to reality with no hills or aero resistance.

Overall remember that for the average person with a "normal volume" exercise routine accuracy is nice but not necessary for the purpose of calorie counting for weight control. I lost perfectly well using an indoor spinning bike's displayed calories despite in retrospect realising those estimates were probably 100 cals too high. It would have taken 35 sessions to skew my weight loss by just 1lb.

To answer your question directly I've used Polar HRM linked to Strava and Garmin apps. Garmin and bike bike computers linked to the bike. Wahoo HRM linked to Wahoo app. Wattbike Hub app linked to Wattbike indoor bikes.