How are redirects, rewrites handled in EpiServer DXC? Is there some utility that EpiServer provides that is like bitly
The user manual and the DXC Service documentation are good places to start:
Vanity URL (simple address): https://webhelp.episerver.com/latest/getting-started/on-page-edit-view.htm
Redirects (shortcuts): https://webhelp.episerver.com/latest/cms-edit/all-properties-view.htm#Settings also https://github.com/BVNetwork/404handler
Rewrites: You can use the standard URLRewrite module with the appropriate rules configured in web.config, example here: http://world.episerver.com/digital-experience-cloud-service/going-live/#RedirectingHTTPS
There is also a commercial product my company built, called SEO manager - it's a URL manager where you can define custom 301 redirections from edit/admin mode, define simple addresses, etc. Also, when an editor moves a page, these redirects are automatically added without a need for user actions. There is a way to import URLs from the old site and redirect them to the new one.
If you are interested, take a look at https://www.mogul.com/en/about-mogul/products/seo-manager/