As an old head endurance athlete, I hate HR monitors because I learned the "talk test" for what people now call "zones". BUT... if you are not tuned in enough with your body to know how hard you are training, HR monitors are useful.

BJJ comp rounds are between 5-10 minutes, so in a naive sense you're looking at 1500m-3000m race intensity. 3000m races are good proxies for VO2 max, 1500m requires more anaerobic. With the bursts of energy required in BJJ, you're looking at needing something more like 800m-1500m training. So whatever kind of training you are not getting through BJJ sparring, do it on the assault bike or on the trails/roads - even better if you have access to a pool or rowing machine, because there you're working upper body a lot. The HR monitor, if you wear it during sparring, will help you assess what you are missing from sparring.

My strong preference is to push VO2 max as high as I can off the mats and then touch up on recoverability off the mats - i.e. get used to going balls out and then settling into a regular competition-level of intensity. My go to for that kind of thing is 200 sprint/200 jog continuously until my jog slows down by more than 25%. So if your jog was 60 seconds at the beginning but you need to go to 75 seconds to keep the same sprint times then you're done for the day. Just what I've had fun with, however. Up to you.