Hi, sorry to re-raise this old thread, but I have the exact same issue, and it's spreading!
This morning on one machine which still worked for pasting with enter key, after a reboot it's stopped working, on 2 other machines the enter key stopped pasting a while ago, all have been running office365 (so excel 2016) for about 18-24months, all from the same family office account, all updated regularly, so currently on version 1711 build 8730.2122
Tried to do a full repair (using the online option) but that has made no difference.
Checked the options and advanced features, but nothing and having searched google, found little relevant except this post, which the fix did not work ...
Microsoft linked helpdesk (using the help chat option inside excel) got me nowhere, except a sore head : - (
I don't have any clipboard managers enable on all the machines in question, might have on one of them, and do use a KVM screen sharing tool called Multiplicity on them all, but this has not been updated recently, and did not affect the machine that continue to work using enter (until it stopped earlier today!), so can't see that being a factor?
Anyone able to help revert the paste capability to the enter key.
Thanks in advance
Richard