This is not good at all.
A lot of the 2013 models had their engines rebuilt by Mazda. So they should be able to check and find out whether your car is within these cars. I do not think they will need to strip the engine to do a simple ECU scan and find out what is wrong with the sensor problem.
Their guess is that there are serious problems with the engine and it is not just the sensor playing up. The engine does not get dirty if there is no problem. So these cleaning services are not going to fix the problem, you can save the money. They may even make the problem worse by losing up the dirt and blocking up the engine.
Check other material online and you will find out that you are not the first one with this problem. For example:
https://www.youtube.com/watch?v=eJ7W4ssxZZYEven if you remove all this dirt, you have to tackle the source of the problem so that does not happen again.
The service history does not mean a lot nowadays. You take the car in, they replace the oil and they wash the car. It does not cover any preventive work, work that will save you on maintainance later. In addition to that, because the services are sensor based, if you drive the distance, they will extend them. So it is not that the previous driver missed the services but the car did not need one. The legal details of the warranty is another issue though.
If you cannot come to a deal with Mazda to fix the car for free or with a reasonable contribution, you may have to decide whether you are going to pay for the £3.5K repair. Basically you will have a rebuilt engine after that. I am not sure whether it is worthy.
The problem with the finance is that it makes everything expensive. So you only see your monthly cost but at some point you will have to pay the cost plus the finance profit. When a big repair comes up, it complicates the decisions as your monthly car cost is low but the repair cost is high.
Your car is already high on mileage and if you trade it in, it will be sold at the auction. So if you have no error codes flashing, you should consider a straight swap with another car and cut your losses. In that case, don't buy another car from an independent dealer because they source their stock from the auction and you will end up buying another similar car. Try a franchise and aim for a petrol car as you are not doing the mileage for a diesel.
There is a limit on how much mileage you do to help you decide whether the diesel is the right option. Check something like that:
https://www.whatcar.com/news/what-fuel-comparison-tool/If your best fuel is petrol, which means you are not driving a lot, and if you have to pay £3.5 for the engine rebuilt, you could consider swapping the car for an "older" petrol from a franchise, possibly a smaller size like segment C to get a similar age car, that will not need an engine rebuilt, and will help you to clear out the finance. Once you are on the positive side again, you can buy another car if you want or keep building your fund for a rainy day.
You will need to start thinking strategically at this point as an engine rebuilt will not last for ever and as you are not doing high mileage, you may not need this type of car. People with the older generation cars, had their engine rebuilt from as low as 30K miles but then the problem came back. Their problem was a simple timing chain but in your engine, you will need a new crankshaft. There are people who had two timing chains but I am not sure if you can afford to rebuilt your engine twice.
Try the dealers to check what price they are willing to pay for your car. I had bought the car from Arnold Clark and they have an instant online valuation, you just need to provide your number plate and mileage:
https://www.arnoldclark.com/sellThey have a list of criteria at the end to check the condition of the car but there is nothing serious. They just need a car that drives. If you find another car you want to buy from them, they pay you this valuation, they deduct your current finance and they make another deal for cash or finance. You have to consider the £3.5K repair, the interest you have to pay for 2.5 years and the alternative option of getting a car by giving out yours and possibly become free of debt.
The best price you will get for your car is through a private sale but as the car is not right, don't go down that route. All part exchanges will pay you the auction value and not the market value. Check what is the market value of the car from something like Cazana:
https://cazana.com/ukAnd then decide whether your repair is within this limit. If the repair cost is smaller than the difference between the market value and the auction value, you could repair it. Overall it is down to you to decide how much you can afford spending for the car. You have costs like the insurance and the tax that you cannot avoid and then have the cost of the car and the repairs. The insurance and the tax cost should be higher than the cost of the car and its repairs if you keep the car long enough. If you start repairing a car, then you have to keep it for a while for that repair to make sense economically.