I think this may actually be one of the cases where it is too good to be true.
You’ll become resident in Portugal. And as long as Portugal, your tax residency, chooses not to tax you on certain income - even though they “can” (could) according to the applicable DTA - then you just don’t have to pay these taxes. Note that “can” is the usual wording in DTAs, not “have to”.
The common exceptions may be income from assets in the other country (usually business and/or real estate), non-refundable withholding tax and departure tax (which Switzerland doesn’t levy, to my knowledge, as they’re often a tax haven themselves).