Unfortunately your ground preparation was sub-optimal as you have discovered. Instead of killing the weeds, you actually spread them. A lot of weedkillers only kill top-growth, not the roots. And killing perennial weeds with persistent roots like brambles and nettles requires specific measures you can easily google. It was sub-optimal to seed the lawn before you saw what else was going to come up.

Probably a combination of ordinary lawn weedkiller (which doesn't kill the grass) at a suitable time of year and mowing will do for the thistles.

Neither lawn weedkiller nor mowing do for nettles, from experience. Though probably mowing, if sufficiently frequent, would do for them in the end. The only way I have found to remove nettles from a lawn without killing the lawn is tediously to do my best to remove the roots by hand with a hand trowel and careful teasing between the grass. Fortunately the roots are strong and you can pull quite hard before they break, unlike ground elder. I have successfully eradicated them from a small area over a couple of seasons in this way. For killing a larger area, really you'll have to let them grow to have enough leaf area (but don't let them seed) to apply suitable weedkiller, then apply megadeath. Roundup in late summer is said to work. Though some recommend brushwood killer on them. Then reseed the lawn you also killed, once you have verified that the nettle problem is solved.

Lawn weedkiller won't do for brambles, you need brush-woodkiller if you want to kill them chemically. And probably repeated application. But I suspect that regular mowing might be enough to get rid of them eventually.