My understanding is that if a non-UK, non-Irish, non-EU citizen who does not require a visa for the UK or the Republic or Ireland enters the UK via the Republic or Ireland then they are deemed to be admitted to the UK for the remaining duration of their admission to Ireland.
Before brexit, EU citizens had the right to reside indefinitely in the UK and Ireland. This is no longer the case for the UK but Ireland is still a member of the EU.
So what if-anything is the legal status of an EU citizen who enters the UK via Ireland?