I owned a Stag at one time. Retrofitted with a Rover V8 (fairly popular mod). I actually spotted it and spoke to a later owner of it, by which time it had acquired a Triumph straight 6.
The Triumph V8 did get a bit of a reputation but the wisdom within the owners club said that a lot of it was down to early failures and finding casting sand in the block/radiator wasn't uncommon. Looked after they were ok, but could say that of a few engines of the period, A-series, crossflow, etc. Think it was maybe a case that the Rover engine survived neglect better.
More the Stag engine was 2 of the Triumph 4 cylinders. They were never fitted into any other car either. Engines were 2 valve/ cylinder, dolomite sprints had a 16 valve head. I also had a TR7 with a dolly sprint engine in it, ownership overlapping briefly with the Stag. Think there was some sort of link between the Triumph engine and a Saab one too.
Rust bucket? Compared to a modern car yes, compared to a contempary? No worse than the likes of an MG BGT. Must be a mass produced car with one of the highest % of surviving ones left.