Thanks so much for this!
We could have gotten married we have simply chosen to be common-law. I guess my concern is that they will rightly notice that this is quite an unusual thing to do in my partner's country (Jordan), and will have questions as to why we didn't just get married.
We have an AOR and I was thinking of submitting a letter explaining that while we have different religious backgrounds technically, we aren't individually religious at all, nor are we too concerned with Jordanian social pressures, and that is why we didn't immediately prioritize a wedding.
I may have just heard too many horror stories and be totally overthinking though?
You may be overthinking but hard for outsiders to say.
There are occasional cases here of those applying as common law and the validity of the common law aspect not accepted on some grounds. They would often/usually appear to be cases where the common law documentation (cohabitation) was lacking, and/or especially in cases where the period residing together was not much above the 12 month minimum - so if the docs establishing start of cohabitation are weak, no longer meets that 12 month requirement. Longer periods of cohabitation don't seem to have issues much; but note of course lots of common law cases are handled without issues as well, the 'problem' cases may have other issues as well (i.e. not just be the short cohabitation period).
Clear cases of error WILL be refused (e.g. the start date of the residing together simply doesn't match the dates required to get that 12-month continuous cohabitation).
For those residing together for longer periods and solid documentation, should not be an issue.
That said: my personal view is that in some/many cases it may make sense to marry in order to submit as married (whether by moving marriage up or having a smaller civil wedding or delaying application a bit) instead of as common law. (Not all applicants have that option though)
Common law application means IRCC officers are making judgments about the 'common law nature' of the cohabitation - the relationship, and joint household, and other factors - as well as the sufficiency of documentation. It does mean more chance for errors or omissions or examining officers deciding there is something else they think doesn't 'look right'. But for really clear cut cases (many years living together), pretty simple judgment.
In contrast, married sponsorship is first evaluation of 'is it a valid/legal marriage' based mostly on a legal document, then followed by 'is the relationship genuine'. If the couple was residing together for longer periods before marriage (eg common law), then the relationship evaluation is also easier.
My spouse and I first prepared our documentation based on common law due to a minor legal obstacle to marriage but then were able to resolve it and submit as married. We had years residing together and children so I was not concerned really about common law not being recognized - but from my perspective, it was easier and less stressful submitting as married because documentation simpler (country and case-specific factors, some things like joint leases and official addresses are not always so easy). And I suspect it was a more straightforward case for the examining officer as well that the marriage certificate was there (less volume of documentation too).
Again, though, not trying to claim it is necessary or that submitting as common law is a problem in the vast majority of cases; the sponsorship process is long though and in some cases may be worth considering.