How technical should an EM be?
An EM should be technical / “hands on” enough to be a reviewer for design docs and make a monitoring dashboard for the team’s KPIs, but should not be a blocker for reviewing code and should care enough about coaching to delegate writing design docs to the TLs.
Someone other than the EM ought to review all code since more than one person who writes code should have context on all new code. Therefore, I only spend my time reading code when it was the most valuable use of my time. In practice, I spend less than an hour a week reading my teams code because everything else is more valuable: coaching my team on project execution, improving meetings and processes, hiring, and using standing meetings with peers to resolve local prioritization issues gracefully and ensure the organization has a coherent strategy that maximizes the value for the customer.
It’s tempting to be more “hands on,” but that should be a rare thing you do to keep your skills sharp; if being “hands on” is required by your team, you should probably spend your time differently for 2 months to fix that.