There are 2 parts to the bureaucracy that will control your flying career. One is the issuer of the licence that you hold; the other is your entitlement (or lack of it) to live and work in countries other than that of your residence.
Licence: an EASA (i.e. European) licence entitles you to fly aircraft registered in EASA countries, which (briefly) is nearly all European countries except the UK.
However, unless you have the right to live and work in Europe, that will not help you to get a job in any EASA country.
For the UK, to fly a G-registered aircraft (i.e. registered in the UK) you need a licence issued by the UK CAA, a different Authority which since Brexit has had no connection with EASA. And, to get a job here, you would need the right to live and work in the UK.
With a few exceptions (there are some states that recognise licences other than their own, for example in the Middle East) you need a licence issued by the state of registration of the aircraft you want to fly; and you need the right to live and work in the relevant place.
Mostly, the right to live and work is the problem that is the more difficult one to crack.