I created a flow and set it to manual start only. The only action I do is log the Content Type ID of the current item, I get 0x0101006DEBD2FA20532748A13F342889D612ED0081C5511C47941049AF052D0814DC24A3
If I now configure the flow to start when an item is modified and I set the condition to be Content Type ID = 0x0101006DEBD2FA20532748A13F342889D612ED0081C5511C47941049AF052D0814DC24A3 - the flow never starts when I edit the item.
Do start conditions not work?
Ranjith's suggestion is valid and you can use "contains", but i tried with "equals" as well and it works for me.
Can you please let me know if "contains" works for you.