The Verdict: Not eligible
You need no work permit: as an EU, EEA or Swiss citizen you can live and work in Poland freely. If citizenship is the aim, look at our naturalisation route.
The work permit regime and the single residence and work permit exist for third-country nationals. You may take any job or run any business without them.
The one formality is registration. For a stay over three months, register your residence at the voivodeship office and you receive a certificate of registration of residence for an EU citizen. Non-EU family members have their own document and their own right to work.
For the longer term, five years of continuous residence gives you a permanent right of residence. Three years holding it, with stable income, legal title to your housing and Polish at B1, opens recognition as a Polish citizen.