Is there a contract length I'm locked into when I start with a CSP partner?

This depends on the specific partner's own terms, separate from Microsoft's NCE subscription terms (monthly/annual) which apply regardless of partner. Some partners operate on a month-to-month service basis with no additional lock-in beyond the underlying Microsoft licensing terms; others may have their own minimum engagement periods as part of a service agreement.

It's worth clarifying this distinction explicitly — Microsoft's licensing term and the partner's own service agreement terms are two separate things.