Re: "Are there easier Copy-Paste options available on iPhone?"
Apple support have an article online (link below) that may be helpful to you:
See: How to: Select, cut, copy, and paste text on iPhone - Apple Support
Eg says:
Tip: "To move text without cutting or copying:
touch and hold selected text until it lifts up,
then drag the text to another location."
________________________________________________________________________
Re: "Is there a way to add a dedicated copy and paste button to the iPhone keyboard?"
Am no expert in this area, so I don't know for sure, just that "shortcuts" can be created for many things:
(There may be the steps of "select" "copy" and "paste" to consider).
See how to: Use Shortcuts to automate tasks on iPhone - Apple Support
_______________________________________________________________________________________
Re: "Are there any iOS settings, tools, or third-party apps available that can provide a simpler solution
for copying and pasting?"
Sorry I don't know of any, apart from the possible option of shortcuts above. (Does not mean there aren't any.)
If needed: You may want to contact the experts : Apple's Accessibility Support Team:
How to contact Apple for accessibility support - Apple Support
or
Apple's Accessibility Support Website (info / support / contact options etc.)
(NB: You can "Get Support" (online chat / phone / email etc.) from the link at the bottom of their website:)
Accessibility Support - Official Apple Support
All the best :-)