Distribution is often one of the hardest portions of mobile applications and should often be considered during the design phase of the application lifecycle so that when you come to this point in the journey you and your client will be satisified with the results.
With that being said, there are two primary questions you will need to answer.
1. Who is your intended audience for this application? I only ask this because you mention the Enterprise Program which makes me think you do not want for it to be available on the App Store.
2. Does this meet the Apple App Store Review Guidelines? I ask this because I think your best option is to use Apple Custom Apps.
Depending on how much long term support your company wants to offer, typically your MSA/SOW would define the deliverables which usually includes source code (we always have this at our organization) and a compiled version of the application.
If the company that you are developing the application for does not have an IT Department that understands management and distribution with an Enterprise Certificate, but does have an MDM, I would recommend using Apple "Custom Apps" on the App Store and having your customer use Apple Business Manager to manage the distribution in house.
If the comapny does have an Enterprise Certificate, then simply provide the IPA to them for distribution. However, it is agains the Terms and Conditions of the Enterprise Developer Program for your company to sign an IPA with an Enterprise Certificate and then provide it to another company for distribution and consumption. Many developers have abused this as seen in the news which is why the program is being phased out. You also do not want to be responsible for this because then the company you have developed the application for will always come back to you needing a newly signed version of the IPA and any other certificates which could in turn compromise your account.
Those are the only two options that stand out as functional and repeatable with little involvement of time and cost.
Codesigning is a different topic for these platforms, hopefulluy the above helps lay out a simple road map to ensure that you and the company you are developing for have long term success.
Hopefully this helps!
Thanks a lot! That definitely pointed me in the right direction.
1. You are correct the app shouldn't be publicly available on the AppStore. It is only for in-house distribution within the company we are developing for.
reading the rest of your answer I also think using Custom Apps and the Apple Business Manager seems to be the best solution for all parties involved.
I'll definitely have a closer look into the topic!