Tested on dmaster.
Give Contact external ID eg fz123456
then set QuickSearch for External ID and enter
fz123 - no result
fz1234 - no result
fz12345 - no result
fz123456 - yay
Ah, see this applies to Internal ID too, namely
2 - Muller
20 - ah.olsen@
202 - demo@
2% - Muller
Can you reset QuickSearch so these match with wildcards?