I can suggest 2 workarounds:
Either drag’n’drop the created file to Files or iCloud, or simply save to Files, then Share/Airdrop from there (though sometimes that share can also break…).
Also, a tipp from one of our colleage:
“For me on iOS 14.x sometimes the os level share menu does weird stuff, like some apps to share disappearing. Besides reboot the workaround I found is to change the system language of the os to something and back.”
Thanks @Laci_K I’ll give those suggestions a shot.
What seems odd though is that after the app experiences a break in sharing, it begins to lag like it’s 2003. And only Shapr lags, until restarting the app.