I brought up this very same subject a few months ago, when we were considering getting a trike and like you, couldn't determine a good way to store it.
Ultimately for the time being, we have decided not to get the trike. However, of all the various ideas that were discussed, the one I liked best that I would probably do, is a solution 'jaycocamprs' posted. Check out his post, along with pictures he posted in the 3rd page of my thread
HERE. Very ingenious way of mounting a tricycle vertically on a regular bike rack. Just may work for you.
One thing to keep in mind: Know the maximum weight your bike rack is rated to carry, and the weight of your trike and other bikes you plan to put on the rack. These trikes can be very heavy, usually about twice the weight of a normal bicycle. I found that I could probably have fit a trike and two other bikes on one regular rack using jaycocamprs approach, but overall weight may be a bit more than the rack was rated to handle.
Will and Cheryl
2021 Newmar Baystar 3014 on F53 (7.3 V8) Chassis ("Brook")
2018 Jeep Wrangler JK ("Wilbur")