Trying to switch my work email with my personal one in this Slack workspace, how can it be done?

Hey Alex 🙂 There are two options. You either can create a new account with your personal email address and rejoin the workspace, or you can change the email address that's connected to this Slack account (Profile --> Account settings --> Email Address).

I've rejoined with my personal account (@Alex Mirkin), is there a way to transfer all the DMs?

We can't transfer DMs, unfortunately transfers can only work with public channel content. If it works for you, you can change the email address on Slack and I believe everything should be saved. If you find any other solution that requires a workspace admin/owner we'll be happy to help!