Why don’t you take the Regiojet train#1031 from Vienna to Budapest
Deli for €9?
Kinko that would most likely be the one the OP is referring to as 1) it goes to Kelenföld not Keleti and 2) while the national trains stop at Kelenföld the price is the same as going into Keleti (or that’s the case on the few I have seen)
But the OP's problem is probably that the OP is buying the ticket from the wrong company. Maybe someone convinced the OP to use the third party TheTrainline or OBB (without checking MAV).
If the OP were to purchase the tickets from the Hungarian national rail site the fare would be 17 to 21 euro plus 2 euro for the seat assignment in 2nd class. I promise the difference between 2nd and 1st is minimal, but if you do want 1st that runs 29 to 39 euro …. Yes, on 13 May.
Go to https://jegy.mav.hu/ to buy the ticket, be sure you also buy a seat reservation. Then download the App on your phone so presenting your ticket will be easy on the train. Note you will an email with your ticket, but it will have two attachments. One is the actual ticket the other is the seat assignment. If you use the app on your phone the conductor will makes short work of any confusion.
Okay, then Kinko’s idea. RejionJet, a private train company. They do start at 9 euro (at 7:30 in the blessed morning), so figure close to 12 euro starting cost for a reasonable time that vs 17 on the national trains. I think the 12 euro includes the seat assignement but not sure about that. The big difference is with Rejiojet you end up at Kelenföld or Deli train station which are both like a big outdoor commie era bus stops …. cause that’s what they are. Still, getting into town isn’t hard as there is an underground <15 minutes, and there are some trams <35 minutes that allows you to see some of the outskirts of the city on the way in. On the other hand the national company takes you to Keleti and grand old 19th century rail station which might be more in keeping with the theme of the holiday if the extra 5 to 7 euro doesn’t bother you. Keleti is also well connected and close to the city center. It’s a matter of preference.