Summary
After falling out of the league, Howard revived his career in Los Angeles in the '19-'20 season, acting as a solid backup center as he helped the Lakers make a championship run. He played decently during the next season in Philadelphia, but struggled to add value to the 76ers during the 2021 playoffs.

At age 35, Howard doesn't have the explosiveness that he once had, but he's strong inside and posts really good rebounding numbers on both ends of the court. He also has very good steal and block rates. He also can still be a deterrent on defense, as his teams tend to force fewer shots at the rim when he plays compared to when he sits. He can also be a decent roll man as long as he doesn't have to dribble before going up with it.

Howard has accepted that he won't get touches in the post, and instead gets his shots off dump-offs and put-backs. His finishing at the rim was down in '20-'21, as the 62% he shot in that area was his lowest mark since his rookie season, per Cleaning the Glass. He did bring that back up to 66% in '21-'22, but that is still below average.

I don't think Howard has done anything to prove he's worth more than the minimum, but he has shown that he can still contribute, and will likely stick around in the league for at least another year.
 
Cap Considerations
Howard will be an unrestricted free agent with a $1.8 million cap hold and Non-Bird Rights. This means that the highest starting salary the Lakers could offer him using the Non-Bird Exception is $3.4 million. This should be enough to retain Howard, since he settled for the minimum of $2.6 million to come to Los Angeles. Alternatively, the Lakers could use their Taxpayer Mid-Level Exception to re-sign Howard if he demands more than $3.4 million.

Other teams will have multiple ways to sign Howard as even teams without cap space could possibly use any of the Non-Taxpayer MLE, Taxpayer MLE, or possibly even the Room MLE or Bi-Annual Exception to sign him. It's also likely that Howard only gets minimum offers.