The use of !important is important () otherwise it would take no effect.
And now you can use it like this, note the no-shadow attribute:
<ion-searchbar no-shadow placeholder="Put some awesome search placeholder text here" type="text"></ion-searchbar>
This will make the styling available globally across the app.
Hope it helps!
Cheers
Unkn0wn0x
PS: Of course you can put the styling of the ion-custom-searchbar.sss directly into the /src/theme/global.scss, but with the solution I mentioned just before, you can keep a much cleaner structure for every component.