Do I need to seam-seal a budget ultralight tent myself?

Yes, often. Reviewers of the 3F UL Lanshan series specifically flag that seam sealing is a DIY job out of the box, and that's a recurring critique of cheaper trekking-pole shelters. Factory-taped seams are more common on freestanding budget tents like the Naturehike Mongar UL and Kelty Discovery Trail.