It’s so simple just to provide a link to an online form that it seems pointless to fret over how forms can be placed in emails. Of course, clients and their whims are always the fly in the ointment. It’s good to have articles like this to point them to, all the same!
I often take my lead on this sort of thing from the major emailing services themselves, and even they don’t like the idea much. See this, for example: https://www.campaignmonitor.com/resources/will-it-work/forms/