test 1 == 2 && echo "ok" || (error_code="$?"; echo "failed with '$error_code'"; exit "$error_code")
It's not so obscure, there is just no native "re-raise" function so you have to record the exit code yourself (actually, bash's built-in exit will return the last command's exit code, but in the example above, that's the "echo" which actually succeeds).
Edit: since the above runs it in a subshell, $error_code is not available outside the parentheses but if you need this, you can try:
test 1 == 2 && echo "ok" || error_code="$?" && echo "failed with '$error_code'"
exit $error_codeWorks in dash/bash/zsh at least; not 100% sure whether the behavior of $? on the command in an if test is mandated by POSIX and/or portable. Note that you can't replace the empty then-branch with a negated condition because the negation also eats the return code.
Also, absolutely correct propagation is essentially impossible (but usually not useful anyway), because some errors might be unexpected signal exits or inability to find the command in the first place, and those will get punned onto other nonzero exit codes. I forget the exact conventions OTTOMH but generally they're in the high half (≥128).
Where texinfo is available, "info bash" is a great reference; "man bash" is everything in a single page — so less manageable — but you can look for BUILTIN section, which documents "exit" built-in function (among other things).