Bought a 2019 BMW with missing service history (dealer claimed FSH) – Need advice

Bought a 2019 BMW 218i from a dealer on 13/09 I was told both over the phone and in person that it had a full service history.

I was explicitly told by the dealer that the car had a full service history. I trusted their word, assuming it would all be logged digitally on the iDrive like modern BMWs do.

Today, I checked the iDrive and BMW's central system. It completely stops after October 2021 leaving a 4 year gap (2022–2025) with zero digital records. No physical servicebook in the glovebox either.

I reached out to BMW UK today with my reg and VIN to double check their central network database, and they confirmed they only have those exact same three franchise visits on file nothing else.

My concerns & questions for you guys:

1. Paper History Concern: If they claim "paper-only" history, a blank iDrive will ruin future resale value, and you can't sync third-party paper invoices onto the official BMW network anyway.
2. Because they verbally promised an FSH and it clearly doesn't have one, do I have solid grounds to reject the car for a full refund? Since it's within the 30 day window and I paid part of the car via credit card.

I don't know what I should do next? I'm going to call the dealership and ask them where is the FSH

Cheers for any advice!