Is saying "I pledge to myself" considered tantamount to a pledge to Allah, and does neglecting to recite Surat Al-Baqarah, which I pledged to myself I would do, entail sin?

Your statement, "I pledge to myself," is merely a promise that does not necessitate fulfillment, nor is it considered a covenant with Allah Almighty. You are not obligated to offer expiation for an oath (kaffarat yamin) if you violate what you pledged to yourself. However, if you offer expiation for an oath as a precaution, it is a good deed.