sets:

model.Tasks          = Set(initialize=unified_data['Tasks'].unique().tolist())
model.specialist     = Set(initialize=unified_data['Name'].unique().tolist())

Variable:

model.Assign = Var(model.Tasks, model.specialist, within=Binary)

Constraints:

task only assigned to one person

def _SingleAssignment(model, task):
        return sum(model.Assign[task, specialist] for specialist in model.specialist) == 1
model.con_singleassign = Constraint(model.Tasks, rule=_SingleAssignment)

Skill Mapping Matrix

def _CanDoTask(model, task, specialist):
        return model.Assign[task, specialist] <= model.Skill_Mapping[task, specialist]

model.con_candotask = Constraint(model.Tasks, model.specialist, rule=_CanDoTask)

no longer than 8 hours

def _TimeConstraint(model, specialist):
    return sum(model.Assign[task, specialist] * model.ProcessingTime[task] for task in model.Tasks) <= 
          8*60 * 60
model.con_timeconstraint = Constraint(model.specialist, rule=_TimeConstraint)

no less than 1 hour

def _MinWorkHours(model, specialist):
    return sum(model.Assign[task, specialist] * model.ProcessingTime[task] for task in model.Tasks) >= 3600 * 1
model.con_minworkhours = Constraint(model.specialist, rule=_MinWorkHours)

Objective:

  def _obj_competence(model):
        return sum(model.Competence[task, specialist] * model.Assign[task, specialist] for task in model.Tasks for specialist in model.specialist)
    model.obj_competence = Objective(rule=_obj_competence, sense=maximize)

Adding the _MinWorkHours constraint causing the infeasibility, even without the _TimeConstraint constraint.