As a military helicopter pilot in the 70s, I sure hope your mower is nowhere near as loud as the UH-1N helicopter I flew. They are noisy, either inside or out, and long term exposure leads to hearing loss for many. I always wore earplugs inside my helmet and I still had loss when I left the service. However, back in the 70s the military wasn’t that careful about noise exposure and the USAF jet pilot helmets we used didn’t provide as much hearing protection as the Army and Navy helicopter specific helmets from the same era.
A current helicopter headset has significant passive noise reduction that may be enhanced by electronic noise reduction. For example a David Clark H10-76XL military type headset provides 24 dB of passive noise reduction (NRR). The electronic noise reduction provides 17-22 dB beyond the passive. The headset is large and fits over your ears sealing against your head - that helps with the passive reduction.
Finding specifications for Bose equipment isn’t quite as easy, especially for consumer level equipment. Quickly looking at the Bose page for the hearphones, I don’t find a specification for the noise reduction, either passive or active. In any case, I doubt that your Bose hearphones provide the noise reduction of a quality aviation headset, especially those for helicopters or loud general aviation (unpressurized) aircraft.
You might consider wearing industrial type noise reduction muffs when using your mower. You might be able to wear you HAs inside the muffs (I wear mine inside some large headphones that provide 20+ dB of passive noise reduction). If the HAs are MFI or bluetooth, you could possibly hear your phone or streaming music with high NRR muffs.
I hope your hearing stabilizes and you find a solution to the noisy mower.