Interest rate targeting uses an unemployment buffer to keep wages and therefore prices under control. Poverty for those in work is entirely part of the plan. To fix the poverty problem you need to fix the structural viewpoint and return to the Beveridge condition - everybody must have an alternative living wage job offer available to them so that job competition works properly in favour of people. There must always be more jobs available than people that want them, not slightly fewer.
But that then runs into what Kalecki called "The Political Aspects of Full Employment" - a recommended read if you haven't already: https://mronline.org/2010/05/22/political-aspects-of-full-em...
Truly a 'wicked problem' - tied up with the concept of power
Its a kind of thing like the average number of hands per population is less than two. Seems counter intuitive, but when you think about it, it does make sense. One shouldn't relay on the expected value of people having two hands, for global population it's a tad lower.
The reason 5% is considered full employment is there will always be a number of people who are unemployed because they are between jobs, for instance their partner has moved or they are rejoining the workforce after pregnancy or even looking for their first job.