Finally! Thank you Microsoft for making this feature more obvious in Teams desktop:
Despite all my best efforts to stress the importance of replying to existing topics in order to keep like messages together, people still started New conversation instead. This breaks the messages into two (or more) buckets and makes it challenging to follow a cohesive thread.
Now the 'New conversation' option is a button you must click to access. Hopefully this will make it less confusing and decrease the number of accidental new conversations in Teams.
Remember, only start a new conversation if you want to discuss a completely new topic. If you do, it's best practice to give your conversation a subject line. Click the A icon at bottom left to do this - it makes things easier to find later.