Why it happens
Slack's desktop app hands every link to your Mac's default browser. Slack has no setting for which browser or profile to use. Chrome then opens the link in the profile whose window you used last. Click a Slack link right after reading personal mail, and it lands in your personal profile.
The same happens with links from Mail, Outlook, Teams, Notion, Linear and any other app.
Quick workaround
Click a window of the right profile just before you click the link in Slack. Chrome then treats that profile as the last one used. It works, but you have to remember it every time, and it breaks as soon as you switch profiles in between.
Send every Slack link to your work profile
If everything in Slack is work, a link router can send all links from Slack to one profile. In Profile Porter, open Settings › Sites and, under Apps, add Slack with your work profile. Links from Slack now always open there, whatever window you used last. A site's own rule still comes first, so you can send, say, spotify.com elsewhere.
Or let each link find its profile
If your Slack has both work and personal links, an app rule is too blunt. Without any rule, Profile Porter opens each link in the profile where you're signed in to that site and use it most, which it reads from your browsers on your Mac. The GitHub link goes to Work, the YouTube link to Personal. When it can't tell, it asks, and remembers your answer.
Hold ⇧ (Shift) while you click to choose the profile yourself, and if one ever opens in the wrong place, click Undo in the notice, or press ⌃⌥Z to move the Chrome tab to another profile.
Get Profile Porter for €12, once.
Everything included, no account, and a full refund within 14 days if it isn't for you. macOS 14 or later; Windows is coming to the Microsoft Store.