The only other Z3 I've seen with rotted trailing arms had areas of serious rot elsewhere. From memory it had gone at the back of the rear inner arches. And showed evidence of the inner/structural sills having gone.
That was on a 2.8 that had 1 previous careful local owner known to the current owner. The rest of the car was lovely. It had spent its life being driven around country lanes accumulating mud and silt.
You ought to check the rest of the car properly before investing further in this. Proper inspection would require removal of the wheel arch liners and sill covers. It's very doable but is 2-3 hours work or probably longer if you've not done it before.
For your own sake I have to say this. It sounds like it's beyond economical repair before you have even discovered the state of the inner sills/arches
If it was on a 2.8 it would be more viable. But as a 1.9 with 13 previous owners it has a ceiling price. I'm guessing it has mileage over 100k. So it will be worth closer to £1k than £2k.
The most viable non-welding repair would be to replace only the complete trailing arms. You might get those for £100 or less a side. But it's still several hours labour and probably running out close to £500 total.
But that's supposing there is no rot elsewhere.
