I have no actual experience of calling out breakdown services for a flat tyre. But dont think they use sealant. I think they carry 'universal' emergency wheels which, by using adapters ,can fit most cars .A bit like 'spacesaver' spares they are only adequate to limp slowly to the nearest tyre fitter.
I think you only have it on loan for a short period .You may even have to follow the breakdown van to their nominated tyre depot and return it to them there. Or they might call out a mobile tyre fitters.
Very inconvenient, with delays, especially out of hours, plus if the tyre needs replacement (often the case) you are of at their mercy for whatever they wish to charge for your replacement/repair , and whatever tyre they have available.
Far better to carry your own spare ,either full sized or 'spacesaver' . If you need assistance fitting it you can call out a breakdown service to do just this, and you are free to continue your journey with no more delay, and get the tyre fixed at your convenience.
Tyre repair gunk comes in two main types. The Honda canisters are a thick goop that coats the inside of the tyre with a thick coating. Most tyre fitters will refuse to do a puncture repair if this has been used and you will need a new tyre.
The other type ,often sold as puncture repair tyre /inflation aerosols, such as 'holts tyre weld ' only inject a thin solution of pva type glue that will seals some minor leaks, and inflate the tyre. . . Not so effective but fairly easy to remove if a puncture repair is possible.