Can other clubs sign him as well or do we have first rights?
And is there a time period or window we need to wait for or can he sign with anyone anytime?
Free agent means he can sign with anyone under any terms any time, with caveats. Free agency signing starts in March. The cards could make him an offer he can't refuse before that and they might, but if not he will likely sign with the highest bidder in March. There is a risk reward to a player waiting for free agency just like there is for a club to sign before free agency.
Once free agency happens you are open to a bidding war as a club. However, a player might over play their hand and wait for offers, not get what they expected and could have got a better offer from their current team and that offer is no longer on the table and you end up playing for less. It's all part of the dance and that is why their agents are paid to get them the best outcome.
Where things get more tricky is unrestricted vs restricted free agents. With restricted FA you get into draft pick compensation and first right of refusal and such. IIRC this is Drake's 4th season so he would be unrestricted.