Can I keep using my current phone while leaving an upgraded iPhone unused as a gift?

Yes, you can keep your SIM/eSIM in your current phone and leave the new iPhone in the box until you give it to him.

For unlocking, new Koodo phones get a 60-day security lock that lifts automatically 60 days from activation. Since the iPhone won't be used on your line, I would recommend unlocking it through Koodo Assist before you hand it over, just type "unlock my phone" here https://www.koodomobile.com/en/help/?autobots=rollout&intent=unlock

More info https://www.koodomobile.com/en/help/unlocking-your-phone

Your brother can double check on the iPhone under Settings > General > About > Carrier Lock. If it shows "No SIM Restriction", it's unlocked and he can use his own carrier's SIM or eSIM.

As well, keep in mind the Tab for the phone stays on your Koodo account until it's paid off.

According to this post, Koodo will start to temporarily lock their phones for a period of 60 days if you purchase your phone on a Tab plan.

If you do not plan to give it to your brother any time soon, it should not be a problem. Otherwise, he will need to either use Telus, Koodo, or Public Mobile as their existing carrier or wait until the period is over before he can use it with another carrier. This is something you may want to consider as a precaution.

Such a silly reason to re-introduce phone locking.  Like organized crime can’t wait 60 days for the phone to unlock.