A great article about how good autistic people can be at sports: https://www.si.com/sports-illustrated/2016/11/01/people-with-autism-spectrum-disorder-embrace-sports-athletics
For those of us in good health sports can indeed help a lot with depression, anxiety etc. and of course also with keeping us fit. However, if you are not very fit, even going for a walk can help. We do sometimes when we feel really bad and it usually helps.
If you are interested in sports maybe Special Olympics can help.
Some of our old blog posts related to sports: