My car is the first I’ve had with no spare, it came with a bottle of sealant and a little compressor.
Had a very slow puncture right in the middle of the tread, no nail or screw and so fixed it as directed. Frankly I was going to keep driving that tyre until it’s all out (Until MOT in November when both fronts will be replaced)
Any reason why I shouldn’t as replacement now seems an unnecessary expense.
I would have taken the car to a garage to get the puncture sealed properly instead of using the sealant as I think the sealant kits are regarded as an emergency ‘get me home’ temporary fix for a faster puncture.
The “Slime” stuff (same s as MTB) is water washable so you shouldn’t get problems with a tyre company, though most of the OEM stuff isn’t so be cautious as spoon says as it can be costly if they are new tyres (which you said yours are not anyway)