The honest answer is the science on this is pretty mixed. Blue light itself probably isn't the main culprit behind screen fatigue - it's more about eye strain from staring at screens without breaks, reduced blinking, and screen glare. That said, some people do report feeling better with blue light filtering lenses, though it's hard to say if that's the coating actually working or just placebo paired with finally paying attention to their eye health.
If you're getting constant fatigue by 5pm, I'd try the free stuff first. The 20-20-20 rule actually works - every 20 minutes, look at something 20 feet away for 20 seconds. Adjust your monitor brightness to match your surroundings, position your screen at arm's length, and make sure you're not in a dark room with a bright screen. Sometimes just tilting your monitor down slightly or using a matte screen protector makes a real difference.
If you still want the blue light lenses after trying those things, go for it - they're not harmful and the extra cost is usually pretty reasonable if you're getting new glasses anyway. But don't expect a miracle. Plenty of people add them and notice nothing. The bigger win is probably getting an eye exam (which you should do if it's been a while) and being more intentional about taking actual breaks from screens.