Any new players added on Yahoo would have been on 2 days waiver, so Sanderson would have passed through it to be available for pickup. If he was already in the system, then he would have been immediately available upon signing. He would have been ineligible if he signed with Ottawa and is then assigned to the minors (or the contract starts in 2022/23).
From Yahoo's news update, the last sentence states that Sanderson joins the team directly after signing (not assigned to minors), thus he is available for pickup.
Sunday, 9:45 am
Jake Sanderson has signed a three-year, entry-level contract with the Ottawa Senators.
Advice: "We're very pleased to get Jake under contract," said Senators GM Pierre Dorion. "An important cog to our future on defence, Jake is an effortless skater who possesses all the tools to be a complete NHL defenceman. A mature leader despite his young age, he played big minutes in college with a blend of poise and confidence. While he still has progress to make in overcoming a current injury, we are hopeful of seeing him in our lineup before the end of the season." Sanderson reportedly had hand surgery in mid-March, which cut his sophomore season short with the University of North Dakota. He amassed 41 points (10 goals, 31 assists) in 45 career collegiate contests. The Senators chose Sanderson with the fifth overall pick in the 2020 NHL Draft. He will join the team this week and could make his NHL debut at some point before the end of the 2021-22 campaign.
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To be clear based on the comments, injuries could have a factor for N/A pickups based on the example in the wording of the CBA.
b. Not Active (NA) players are ineligible to be added to a roster unless there is confirmed news that the player is becoming active (e.g. called up,
activated from injured reserve, served the last day of their suspension).
So if a player were to be injured and Yahoo states them as N/A would mean they are ineligible for pickup, although not 100% sure exactly what status that player is deem to be to deserve N/A (perhaps minor league stint after a long injury before activating to main roster).
Hope that clears things up.