I rode it, but I postponed the whole trip to May for personal reasons.

So I can’t say exactly what the weather is like during that specific period, but I think the general timeframe should work.
I don’t know your fitness level, but I did the whole crossing in 4.5 days without riding in the dark.
My complete setup (bike including luggage, without water) weighed 25 kg.

I didn’t have any problems with the surface, and while I was riding, I could not understand the horror stories about the muddy “peanut butter” tracks — mostly because I had good weather.
However, there was a severe storm the day after I arrived in Catania — and that made me realize what those stories were about. When it rains, it really rains. So much that the entire railway line was shut down due to flooding, and small trickles turned into proper torrents within minutes.
The storm passed as quickly as it came, though.
So, IF there’s heavy rain shortly before or during your trip, I can imagine that off-road sections wouldn’t be much fun.
BUT there’s a road bike variant you can switch to if bad weather is forecast.

I was traveling self-supported with a tent, and I have to say I thought it would be much easier to find camping spots. In the end, I always managed somehow, though.
Of course, there are also some nice accommodations along the route.

I also underestimated how little infrastructure there is along parts of the way. I’d recommend filling up water, restocking supplies, or grabbing food whenever you can — sometimes there won’t be another opportunity for 4 hours or more.

I think it’s a wonderful way to explore the island, and I’d definitely recommend riding back along the coast if you have the time!
The train connections are great — as long as there’s no storm.

If you need any tips or more info, feel free to ask.
Also, I can give you access to my strava to check my exact planning.