There are devices called gutter guards that allow the water to enter the gutter/drain but the debris continues over the gutter and off the edge of the roof. Not sure if you could get one of those for your conservatory roof but you might try looking into them.
The diagram you showed is fine. That is really all you need to do. I might add a small strip of 1X2 along the wall as a nailer for the soffit. The only alternative would be substituting a vented soffit panel for the solid soffit. Using a vented soffit would help a little in exiting hot air and give a bit of ventilation. Best used with a ridge vent for really good ventilation, but better than nothing if used alone.
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It would be worth finding a thatcher - if only so you have someone who will repair/replace the roof when the time comes.
A good one will be able to tell you what maintenance work you need to have done and which tasks you as householder can do.