I have a project schedule template made using Conditional formatting rules.

What i would like to do is change the color of the bar based on the text under the Assigned to column

I got it from this Microsoft link. Simple Gantt Chart | Microsoft Create

You're going to have to adjust the conditional formatting.
It's the conditional formatting (CF) which currently gives a purple colour and applies to the whole range I7:BL33.
1. You'll need to reduce the applies to range to the first section of rows and adjust its colour fill, then
2. duplicate this CF, then adjust the range it applies to, and its fill colour.
3. for each different colour you want.

Not something I'd look forward to doing but it's not that hard.