Can a 3 phase appliance (commercial convection oven) be converted to single phase?

Many can, depending on how they are built. A 3 phase oven usually is nothing more than three single phase heating elements.

Be sure there is not a 3 phase fan motor, or some other 3 phase device in the oven.

Also be sure to understand how to do the load calculations, as the amp draw will change.

A 30 KW 3 phase unit will draw 75.79 amps at 208 volt 3 ph.

A 30 KW 1 phase unit will draw 144.23 amps at 208 volt 1 ph.

To size the feeder, increase the load by 25%.

One other issue is UL Listing. If the unit is built and labeled strictly 3 phase supply, then using single phase to feed it will violate the UL Listing, and you legally will not be able to change the feed.