Q: Should I contact the associate editor (AE) if the status has remained 'Under evaluation' for a month?

This is unusual. Manuscripts typically don’t remain under internal evaluation for so long, if this is indeed an internal evaluation. (Internal evaluation is the check for novelty, basic quality, match with journal’s focus, and adherence to guidelines.) And it’s unlikely that this is the peer review. (Sometimes, journals conduct the peer review internally, if they have the required subject area expert.) Perhaps the AE is busy or unavailable, or in some cases, there could be a challenge of some sort at the journal. So, it’s quite fine to write to the AE seeking an update. Hopefully, they’ll respond and inform of the next action. So, you should go ahead. For which, you may find the following handbooks helpful:

• A practical handbook of templates for communicating with the journal
• A guide to understanding journal statuses

All the best for the next steps!