You literally only need an EU passport though if anyone asks after 90 days.No that's not right at all. The EU allowed visa free travel between countries. It certainly still had restrictions! After 90 days/3months EU members visiting another EU country usually had to register.
Residence rights when living abroad in the EU - Your Europe
Rights and requirements for lawful residence of EU nationals in another EU country: workers, students, pensioners, jobseekers etc.europa.eu
As an EU citizen, you have the right to move to any EU country to live, work, study, look for a job or retire.
You can stay in another EU country for up to 3 months without registering there but you may need to report your presence. The only requirement is to hold a valid national identity card or passport. If you want to stay longer than 3 months, you may need to register your residence.
In many EU countries, you need to carry an identity card or passport with you at all times. In these countries, you could be fined or temporarily detained if you leave your identity documents at home - but you cannot be forced to return to your home country for this reason alone.
On a British passport now, as opposed to before, if you exceed the rules you need a visa or permit. I know of people who work within travel sector who are struggling with this.