Your question is a bit underspecified... ECDSA by itself isn't an implementable protocol: you also need to specify a curve and an encoding for the values at a minimum and ideally a hash function too.
The common DER encoding used for ECDSA signatures introduces several behaviours similar to the ones being discussed here which differ between implementations. (Or, rather, DER itself doesn't but BER does and what things that implement DER usually implement is some subset of BER and some superset of DER).
For curves with a cofactor similar issues also probably arise there-- I haven't thought much about that since I just try to avoid cofactor generally, because it's a pretty big footgun. :)
ECDSA implemented as Bitcoin does today (post BIP66) with a perfectly strict and completely specified DER encoding-- a near-power-of-2-size cofactorless curve-- and an additional requirement on S being in the lower half of the range doesn't have these issues. ... except to the extent that someone could try to make an implementation copying some off-the-shelf-ecdsa and miss those specific requirements and only be partially compatible.
The common DER encoding used for ECDSA signatures introduces several behaviours similar to the ones being discussed here which differ between implementations. (Or, rather, DER itself doesn't but BER does and what things that implement DER usually implement is some subset of BER and some superset of DER).
For curves with a cofactor similar issues also probably arise there-- I haven't thought much about that since I just try to avoid cofactor generally, because it's a pretty big footgun. :)
ECDSA implemented as Bitcoin does today (post BIP66) with a perfectly strict and completely specified DER encoding-- a near-power-of-2-size cofactorless curve-- and an additional requirement on S being in the lower half of the range doesn't have these issues. ... except to the extent that someone could try to make an implementation copying some off-the-shelf-ecdsa and miss those specific requirements and only be partially compatible.