Is it possible that something can be ‘outside’ of the ‘space time’ continuum?

Obviously Yes; abstract nouns, are outside the space-time continuum. Mathematics, justice, fashion, arts, science, religion…all abstract nouns that only exist in our mind.

But are you sure you know what the Space-time continuum actually is??

Space (in this context) is the dimension of (relative) position (hence xyz-axis)

Time (in this context) is the dimension of change (hence ‘rate’).

Spacetime is hence the merged dimension of changing position aka, motion.

So anything that is a ‘concrete noun’ (as opposed to an abstract noun) i.e. has a tangible reality – like a quark, or a table or a solar system – has a physical ()relative) position, and probably incurs change. And mostly will include change of (relative) position…most things in the universe (maybe all things) are experiencing motion, and all experiences relative motion (dimensions being reference-frame specific).

So anything with a physical presence will always be within the space-time continuum, as you call it.

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Why is time regarded as an extra dimension if it is just an effect (or property/attribute) of 3-dimensional space?

Time isn’t an effect, property or attribute of ‘3-dimensional space’. They are 2 distinct, separate dimensions.

Time is the dimension of change (hence ‘rate’…eg miles per hour…the per hour bit is time calibrating change.)

Space (in this context) is the dimension of (relative) position (hence xyz-axis). In fact, Space is the dimension of static position (because, by definition, it excludes Time).

Merge the dimension of static relative position (Space) with the dimension of change, and hey presto you get Spacetime, the dimension of changing position…aka Motion.

That makes Time a pretty important dimension in its own right. Change is what drives the universe, after all.

I am going to link below to an answer I just posted to a similar question.

I hope this helps…

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If space is absolute no matter the frame of reference but time is relative based on the frame of reference of the observer, should quantum superposition be interpreted as a particle in 2 or more places/states in time simultaneously instead of space?

Is space absolute?

Space, the word, has different meanings depending on context.

When you talk about Space and Time together you are talking in the context of dimensions.

Dimensions are abstract frameworks / models, formulated in standard units, that we overlay an aspect of reality in order to calibrate and index that particular reality.

[There are many many dimensions, many aspects of reality, that are calibrated in standard units. Dimensions of weight, mass, density, radioactivity, heat, colour, brightness, sound volume, tone, pitch etc etc.]

All dimensions are relative. And all dimensions are abstract ( eg the dimension of temperature is abstract, heat the underlying reality). And all dimensions must be, obviously, reference-frame specific.

Space (in the context of dimensions) is the dimension of relative position. The XYZ axis, the three sub-dimensions (vectors) of height, breadth and depth, simply determine relative position. And we calibrate in units of, say, miles, or centimetres etc.

And Time is the dimension of change. We calibrate change (rate) in units if time, as in xxxx PER HOUR. The ‘per hour’ or ‘per second’ etc is the calibration of change.

So Time is always used in conjuncture with another dimension to give that other dimension a ‘rate’ of change.

So, Space is the dimension of (relative) position. Time is the dimension of change. Merge the two and you get SpaceTime the dimension of changing position aka Motion.

Spacetime is the dimension of (constant) motion. [‘Constant’ motion (eg miles per hour) because dimensions are reference frame specific…for changing motion (acceleration) we need spacetime-time (miles per hour per hour) and for increasing acceleration its spacetime-time-time (eg miles per hour per hour per hour) etc]

https://qr.ae/pG60xJ