This 2 day plan is built around geography, not just attraction ranking.
Day 1 stays entirely north of the Arno River. The Accademia, Duomo, Uffizi, and Piazza della Signoria are within a tight 10 to 12 minute walking grid. You move gradually south toward Ponte Vecchio by evening, without crossing the river earlier than necessary.
Day 2 crosses the Arno once in the morning. Pitti Palace and Boboli Gardens sit immediately south of Ponte Vecchio. After lunch in Santo Spirito, you cross back north only once for Santa Croce or Bargello. The day ends uphill at Piazzale Michelangelo, positioned logically after Oltrarno.
Walking distances between major stops are usually 5 to 15 minutes. The only significant elevation change is the climb to the viewpoint.
This sequencing avoids the most common mistake in Florence: repeatedly crossing the river and retracing steps because bookings were made without geographic logic.