@VillageLife
Not so fast. :-) You're absolutely correct that the Schengen Zone was supposed to abolish INTERNAL border controls (e.g. between France and Germany and between Bulgaria and Greece, if they are both Schengen members). I agree with you that this is a very good (or, at least, a very convenient) thing.
Freedom of Movement is an attribute of an EU passport. While a local residence right and visa-free travel right is an attribute of an EU residence permit, and visa-free travel right is an attribute of certain non-EU passports.
Whether you, personally, have such rights depends (as @JimJ rightly points out) on an inspection of your ID documents (passport, EU residence permit). The issue is when/where these checks take place. And, indeed, whether it's an immigration officer function (i.e. at an airport or internal/external land border crossing) or you enable (or require) certain locals to join in (i.e. employers at job interviews, police on routine traffic stops, hospital staff when you seek treatment).
There are some, like @JimJ I suppose, who are big on the too-much-immigration issue and support more stringent internal border controls. However, I don't think it's the official EU/Schengen position. As far as I'm aware, they still want to increase security at the EXTERNAL borders (e.g. Bulgaria and Turkey, or Hungary and Serbia, or Frankfurt airport on a flight to USA), and find ways to cooperate with NEIGHBOURING (non-EU) countries so that they reduce the flows of illegal migrants to their border. While also introducing a better tracking system with the ETIAS (and EES), the EU's equivalent of America's ESTA.
IF you have secure external borders, then, in theory, anyone (like you or me) who wants to pop down to Greece for a spot of sunshine has legal travel rights. Because we're already sitting in Bulgaria as locals (Bulgarian passport/National ID card), or we were legally admitted at the border (with our EU passport, OR our non-EU passport with our EU residence permit, or Bulgarian residence permit, OR our non-EU passport with visa-free travel rights and/or a Schengen/country visa). It certainly seems like a worthy goal, but whether it's possible long-term remains to be seen.
Officially, my Bulgarian residence permit only allows me 90 days in Greece. But with no border checks (between Greece and Bulgaria) I'm not sure how they'd spot my overstay, or what penalties would apply. However, I think it's fair to say that the EU is far less concerned with this type of problem than, say, Somalians (or anyone else holding a non-EU passport that has no EU visa-free rights and strictly require a valid visa) being admitted into Bulgaria.
Similarly, I suppose a (rich) American (or a Brit) flying into Spain has 90 days visa-free. If there are no internal border checks, then he'd have 30-odd countries to hang out in for the next 20 years, as an illegal immigrant. Again probably not the top priority for the EU. And most Brits/Americans wouldn't do this because being an illegal immigrant does have lots of problems (can't work, can't access public health services, can't get a driving license, etc.) AND sooner or later you will hit an external border (or a nosy policeman) and find there are substantial penalties for overstaying the 90 days.
Separately, some countries (e.g. Germany) have introduced (or re-introduced, or never abolished) some border checks. It seems like a politically-driven (i.e. illegal immigration) decision, rather than an official EU/Schengen position. But I'm not a Schengen expert, so I don't know if this is something a bit naughty (I.e. they SHOULD have no border check), or if it's the allowed local implementation decision (i.e. each country can decide whether or not to have a particular check at a particular border). Although that might change, especially if @JimJ is a Euro-MP or otherwise influential (or his views are typical of the majority of the EU population). Or, perhaps, you just need a couple of big countries (e.g. Spain and France) to have full checks at all their borders, for most other EU country to follow suit.