They do not want the high chair
A child who is done with the high chair may eat better in a chair that lets their feet rest. Safety straps still matter if they are climbing.
The seat can change
The plate stays the same: one familiar food, and anything new in a small amount.
Feet that reach something solid often make sitting possible. A stool, a booster, or your lap can be the change. The food does not have to change with the seat.
Climbing
If they are climbing out, the meal is telling you the seat is wrong or the meal is too long. Shorten it, and use a seat they can stay in.
Do not lengthen the meal to win the chair. End it, and feed them again at the next snack.
Away from home
A restaurant high chair may be a no. The familiar food on your lap, for a short time, can be the outing.
Bring the food they accept so the seat is the only new thing, not the food as well.
A sentence you can say
“New seat. Same food.”