Do I have EU citizen rights in the UK if I have entered on my Australian passport (but I am also an EU citizen)?

I have been unable to find an answer to my question on the UK immigration web pages, nor on other travel stack exchange questions/answers, so any help would be much appreciated.
I have entered the UK on my Australian passport. However, since entering I have been granted EU (Czech) citizenship. Do I now have the rights of an EU citizen in the UK?
Basically, does EU immigration law mean that am I strictly bound by the rights/restrictions of the passport I enter the UK on, or do you automatically possess EU rights if you are/become an EU citizen while in the UK, irrespective of what passport you entered on?
Note: I do not have a Czech passport (yet), so I cannot exit the UK and re-enter on that passport. Note: I'm not trying to find out information about the future impact of Brexit, just trying to find out information for the current situation while the UK is still part of the EU.
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Do EU residents have the same rights as citizens?
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.Do I have residence rights in the UK?
you have 'right of abode' in the UK, if you're a British citizen. you're a citizen of Ireland. you have pre-settled or settled status through the EU Settlement Scheme. you have indefinite leave to enter (ILE) or remain in the UK (ILR)Can EU citizen come to UK now?
If you're an EU , EEA or Swiss citizen Irish citizens can continue to enter and live in the UK . EU , EEA and Swiss citizens can travel to the UK for holidays or short trips without needing a visa. In other cases, find out if you need to apply for a visa to enter the UK .What do EU citizens need to enter the UK?
If you're an EU, EEA and Swiss citizen, you can travel to the UK for holidays or short trips without needing a visa. You can cross the UK border using a valid passport which should be valid for the whole time you are in the UK.Rights of EU Citizens (That Many Somehow Don't know!)
Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.
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