That may seem a bit strange, but I'd bet it finds the short value in some statistic (MCV, histogram) ans so can provide very accurate estimate.
-> Index Only Scan using tab_idx1 on tab (cost=0.27..8.29 rows=1
width=0) (actual time=0.043..0.043 rows=0 loops=1)
I'm not seeing how any of the statistic columns would capture a value that doesn't actually appear in the table...(actual ... row=0)
Unless there is some prefix matching going on here since the short value is a substring(1, n) of the longer one which does appear 5 times.
I guess maybe because the value doesn't appear it uses the index (via IOS) to confirm absence (or near absence, i.e., 1) while, knowing the larger value appears 5 times out of 223, it decides a quick table scan is faster than any form of double-lookup (whether on the visibility map or the heap).
David J.