Yes, this information is very crucial to understand what kind of hearing loss you have, in order to have more intelligent discussion that’s more directed and applicable to YOUR hearing loss.
Seb is right that if you wear an open fit dome or CIC with a large vent hole, it’ll let in the lows and mids naturally and provides boost in the high frequency range only. The HF boost provides the clarity and in noisy situation, the loud volume in the low and mid that come through the vent in your HA may drown out the HF boost from your HA, therefore causing the HF clarity to be lost in the midst of the loud low and mid sounds, which directional beam forming will not help in your case because the loud lows and mids still come through unblocked anyway.
If you find the over the counter device more effective for you, that’s most likely just because they’re earbud types or completely enclosed type devices that block out the loud natural lows and mids from coming in and allow you to focus more on the beam formed sound in the front. The HAs can just be as effective (if not even more so) if you just switch over to a more occluded type of fitting to control the volume level of the lows and mids better in noisy situations. Surely it’s a trade off having to put up with more occlusion in order to hear better in noisy situations, but if you’re willing to put up with wearing over the counter devices in noisy situations anyway, it means that you’re already willing to live with some kind of trade-off. You don’t have to go with 100% occlusion, though. Maybe a small vent hole or two maybe a good compromise to relieve some of the occlusion but still provide better sound isolation. My left hearing is fairly normal until 1.5KHz and I wear a bass dome with a single vent hole and I still don’t feel very occluded, so it’s a great compromise for me.
I’m not sure why your providers didn’t suggest this option first (change from an open fit to something more enclosed) instead of pushing you to expensive and antiquated FM Roger pen type solutions. I understand that most people with your type of hearing loss still do OK in noisy situations with an open fit, but not everybody is the same. So if you don’t do well with open fit in noisy situations, they shouldn’t assume that you’re the same as most people and should have tried a different fitting arrangement for you instead of telling you that there’s nothing more they can do for you.
Hopefully you can see now how useful an audiogram can be if posted.