This site and others -- ranging from StackOverflow to Project Euler -- are separate entities and there is no reason to artificially create more correlation between them. What is more internally relevant for math.SE is locating sources for problems or other mathematical material and developing tags that enhance the value of whatever is posted.
A [project-euler] tag would be of interest to users who want to seek or avoid discussion of those problems. (EDIT : this tag exists and has been used for a few questions. I see no reason not to place it on every Project Euler problem that is posted, at least for questions that originate on that site and are not found in other standard sources.)
Tags like [putnam], [AMM], [olympiad] or even [international-olympiad] would help label material from other problem banks with their own special characteristics.
An [unsourced] tag would speed the identification of problems from any unspecified source, including Project Euler. Alternatively, a [sourced] tag would promote the use of sources for all material, including that from Project Euler.
Math is different from programming. What works (or does not work) on StackOverflow, where questions and answers are time-dependent, time-sensitive and contingent on particular software and hardware environments, does not work as well for a math site. Mathematical information is mostly "eternal" and can be cited by reference. It is therefore cumulative and this creates an archival interest in listing of sources as additional data independent from the Q&A.
This reasoning leads not only to tags but to having a structured, searchable SOURCE field, with its own set of tags and forms and check-boxes, as part of the question data. As long as the current SE platform lacks such features, intelligent use of tags can help.