@Luna2 what exactly are sales reps doing when they receive a contact / when they qualify a contact? What you shared is unfortunately too high level to make a recommendation – it’s a bit of a black box currently as to what is behind each lifecycle stage, lead status etc.
Generally, both leads and deals can be managed nicely in the sales workspace. There are tabs for both leads and deals, so it’s not a lot of switching around. Unless the SQL stage is super short (and I can’t currently speak to that due to lack of context), I would recommend using the lead object. Sales reps could review their new SQLs, qualify, disqualify. Qualified SQLs would create deals which would be managed just one tab away.