In Canada, does the expression "I'll pick up your slack" have negative, derogatory or positive connotation?

I'm an American.

If someone is "picking up your slack," they are taking on the work that you are not doing. There's not an inherent connotation about why you aren't doing that work. In many cases, you have slack to be picked up because you're overloaded and too busy doing something of higher priority.

To my knowledge, "picking up slack" and "slacking" do not have a relationship.

The (real, this time; n.1) origin of the phrase comes from sailing. When a sailor is pulling on a "line" (a rope), there's likely to be some amount of slack in the line he's putting down. Another sailor is needed to "pick up the slack" and ensure the line doesn't get tangled. In this context, "picking up the slack" is purely about teamwork; the first sailor is unable to pick up that slack because they are busy adjusting the line, so the second sailor is needed.

Contrast these two statements:

"I'll clean up the mess."

"I'll clean up his mess."

The former leaves the source of the mess completely ambiguous, and no accusation of who made the mess is evident.

The latter places the responsibility for the mess on someone, which could lead to conflict.

In the example you cited, "slack" isn't attributed to anyone. Perhaps it was due to bad luck, game latency, or a loose cat on a keyboard. We don't know. The speaker is simply saying "I got it covered."