You won't need a visa to travel to the EU. You'll only need an ETIAS, for which the application process is far less rigorous.
There is no official list of 'banned offences'. Any such list that you've seen is almost certainly one hosted on a commercial website (of which there are many), which is hoping to make money from gullible travellers through 'assisting' their ETIAS applications once the system is up an running.
However it would seem extremely unlikely that your conviction for GBH would cause you any problems. The
official website indicates that around 95% of ETIAS applications should be granted instantly, with nearly all of the remaining 5% being granted after manual checks:
https://ec.europa.eu/home-affairs/system/files/2022-03/European%20Travel%20Information%20and%20Authorisation%20System-ETIAS-memo_en.pdf
As your offence wasn't one involving things like terrorism, people trafficking or large scale drug smuggling, it seems extremely unlikely to me that it would present you with any problems when it comes to obtaining an ETIAS.
As you've correctly indicated, where you can demonstrate that there was no intent, GBH is not regarded as a crime involving moral turpitude by the US authorities.
https://unlock.org.uk/advice/identifying-whether-my-offence-is-a-crime-involving-moral-turpitude-cimt/
So you wouldn't be subject to an automatic ban on entry. However you'd still be ineligible for travel using an ESTA, meaning that you'd need to apply for a visa. For that, as well as completing the standard application form, you'd need to get hold of your ACRO Police Certificate
https://www.acro.police.uk/Subject-access
and complete this form:
https://uk.usembassy.gov/wp-content/uploads/sites/16/2016/08/VCU01_London.pdf
You'd then need to wait for an interview appointment at the US Embassy in London and then wait again to find out the result of your application.
All of that would need to be done before booking travel to the USA. As the current waiting time for an interview at the US Embassy is 130 days
https://travel.state.gov/content/travel/en/us-visas/visa-information-resources/wait-times.html
you'd probably need to allow up to 6 months for the whole process. Adding on perhaps another 6 months between booking your travel and actually flying out (in order to get the best prices), probably means that it would be best to start your visa application at least a year before your intended date of travel.