Summary
It looked like Gibson's time in the NBA might be over after he was waived by the Knicks in 2020 and was unsigned going into the '20'-21 season. However, the Knicks re-signed Gibson mid-way through the season, and he has looked like he still belongs. He still moves pretty well, and finishes decently inside on offense. He has nice touch on short hooks and floaters, and has some post moves to create space in the paint. He also still rebounds well on the offensive end.

On defense, Gibson at least knows where he needs to be, even if he's limited athletically at age 36. He also has had an above-average block rate over the past two seasons, according to Cleaning the Glass. You wouldn't want to have to rely on Gibson for heavy minutes, but I think he can still contribute as a third big that can adequately fill in when there are injuries, like he has done in New York.

I was surprised that Gibson got more than the minimum as a free agent in 2021, but I think part of that was more of a favor to Gibson and to give the Knicks more salary to potentially use in a trade. I would expect Gibson to be waived in 2022 and hit free agency unless the Knicks really just don't need the space, or if they want to guarantee his salary to be used in a trade.
 
Cap Considerations
Gibson's $5.2 million salary for 2022-2023 is non-guaranteed, and if he is waived he will become an unrestricted free agent and the Knicks will have no form of Bird rights on him.

If Gibson becomes a free agent, other teams will have multiple ways to sign him as even teams without cap space could possibly use either of the Non-Taxpayer MLE, Taxpayer MLE, Room MLE, or Bi-Annual Exception to sign him. However, I don't expect any offers for Gibson to be above the minimum.