[...] All I can remember from yesterday is
that first I was trying some incorrect replace statements (target of
replace was a set of nodes instead of just one node) before using
delete/insert statements ('cos I needed to replace a set of nodes).

You could use an iterative approach, i.e.

for $i in //node
return replace node $n with <newnode/>

This serves as a general solution for similar issues, as an insert or
rename statement only allows single target nodes as well.

If it helps, when I attempted a query in the UI yesterday (instead of
JAX-RX), the database consistently threw some exception and suggested
filing a bug report (I did not, unfortunately, store the details and the
exception, so do not have access to the same right now).

Interesting ... my first guess would be that there was some kind of
concurrent access between the BaseX server and the GUI version.
Make sure you don't use them on the same database at the same
time as this could lead to concurrent file access on disk. Although
possible, it is not intended. We will try to state this in a clearer manner
on our website/documentation.

My comments about insert were incorrect anyway, apologies for the same -
I was mistakenly inserting into the parent element of the actual
intended location (but was later checking the existence in the actual
intended location)

No worries.

If it happens again, will be more meticulous and will store the various
steps/logs. I was using BaseX 6.5.1, will upgrade to 6.6.2 now.

Good to hear. There are a lot of changes between different revisions and
we're constantly improving the code base. So running the most recent
version is highly encouraged.

Feel free to ask for more, regards,
Lukas