Yeah, this is something many climate advocates say - that it is better to keep the car you have - but I don’t think this is backed up by data at all. It’s very clear that that EVs are able to save more carbon emissions than in a fairly short period than you would save by not continuing to drive an ICE vehicle, with manufacturing included.
If we were going to have a simple rule, replacing all ICE vehicles today with EVs will be far better for the climate than keeping them.
There are so many factors that play into that, including the energy mix of the country you live in and so on.
The studies I have seen are a bit suspicious as they seem to employ figures that just so happen to support the idea that buying new cars (EVs in this case) is good. This is not to say that these figures are false, but they fit a bit too well into what the likely funders of these studies want to hear.
The real answer is probably: drive less, and only if you absolutely can not do that, maybe consider getting an EV instead of continuing to use your current ICE car.
