I have done a bit of googling and found that and other people have problems with certificates and IOS 15.5. I am not convinced this will be fixed by using LetsEncrypt.
Your sources may be less than reliable...... or your question might be 'neutral' if you are looking for the answer you want rather than the answer that makes most sense.
So, yes self signed issues almost certainly, and no as JP said, LE certificates are trusted. Self signed are not. So convince yourself that they will be a better solution.
I have lots of Apple equipment (amongst a host of other kit) and none of it has issues with LE certs. I think the real issue is you don't want to believe that because you don't want to learn.....
In addition it seems like using LetsEncrypt will cause you to re-new and then manually restore new certificates on the Iphone every 3 months or so? Anyway, for now I will use the fallback solution of accessing my mail from the Iphone using webmail. Webmail works well for me, I am not dependent on using the standard Iphone mail tool.
Again your sources are less than reliable. The certs get automatically renewed every 3 months, but that is all handled automagically by your equipment - both server and clients. It is seamless and transparent and no manual intervention is required. it just 'works'.
The only time you would have an issue is if there is a renewal failure.
If you have a static IP it is very a simple to do. If you have dynamic just make sure it is updated with the ddclient contrib.
Time to ditch those self signed certs and move on - some of us have for several years now!!