Hi,
I'm hoping someone can help us with some car knowledge/wisdom.
I bought a 2015 Mazda 3 in November last year from a local garage. Within a week or so we reported that something didn't feel right, it sounded like there was a ticking noise in the engine and it didn't drive well in low gears, also the exhaust had been smoking on a couple of occasions. The garage let us take it to their mechanic/garage, they assured us it was fine and that smoke was possibly because it hadnt been driven for a while. We kept driving the car, we only have short commutes to work or school and the car wasn't amazing but it was OK. In early March we started saying we need to take the car back, something isn't right, then before we knew we were all in lockdown.
​​​​The car garage is still closed that we bought it from and we have taken it to our regular car garage. He said the fuel injectors had gone and 'it' was full of sludge. We've just spent near £750 on parts and labour to clear it all up and replace the seals. I've attached photo of our bill.
Car came back from the garage this morning and it still has the same issue we took it in with 2 weeks ago.
The symptom is coughing/jerking in low gears when not accelerating. Most notable when driving through town at about 18mph in 2nd or 25mph in 3rd, when we change gear it stops for a bit and then if not accelerating it starts again. It's not as bad as it was before all this work was done but it's definitely still there.

The car was serviced in September 19 and it had a new mot before we bought it. Strangely we didn't think anything of it at the time but on receipt for the car purchase it says 'oil and filter service' written at the bottom, I remember the salesman saying this but I ignored it because it wasn't relevant when the car had already been serviced in September.

I'm really starting to think we've bought a duff car and am getting at upset at the thought of spending all this money and the car still not being right. Something doesn't sit right about the service in September, another oil and filter change in November and us taking the car back to be checked and we were brushed off.

The car had 6 months warranty from 8th November with RAC but that ran out during lockdown.

Any ideas what to look at next? The car is going back into the garage this Friday for them to look at again, the sales garage is still closed and not responding to emails. I may look into the RAC warranty and see if they would offer an extension because of the lockdown but I'm not sure if that would even be valid now that a non RAC garage has looked at it.
Any help for a novice is appreciated. Many thanks Claire