There’s nothing in Toolbox Pro for this that I can see, and even Scriptable only has read only access to attendees - presumably because attendees update the details.
Calendar invites are usually based around an exchange of a calendar event definition file with an e-mail. It is very often the mail client itself that makes it look more integrated - e.g. Microsoft Outlook can manage both e-mails and calendars together on an Exchange mail server; Gmail is tightly integrated to Google calendar.
But I suspect if you created an ICS file based on your event with the attendee details in it (ref. for those that want it) and then e-mailed it as an attachment to those attendees, it would work.
I’d probably start by creating an invite, getting the file, opening it in a text editor (it is a plain text data format), copying everything out, figuring out what I’d want to populate dynamically in Shortcuts, and then using that content with magic variables in a text action (maybe some additional looping too depending upon what was varying) to build the file. Save that out to iCloud, and then attach that to an e-mail acton set to deliver a covering mail to the proposed attendees; not forgetting of course to add it to my own calendar.
That’s untested, but should replicate what an e-mail client would be doing if you were creating an event manually.