Hello normaliser,
can't say anything about the Primitivo, but walked the Francés this year in april. I'm hardly an expert as I only walked that one Camino, maybe some of this might still be helpful to you, though:
Amount of people:
Apart from easter holidays there were not that many people, and even then, no trouble in finding a bed at all. But you're not walking all alone either. Sometimes there were more people around, sometimes I walked alone for hours, especially in the early morning and afternoon it seemed to be more quiet. Easter is early next year, in march, so the easter holiday walkers will actually be gone again already when you start. From Sarria on more people, but still okay.
Weather:
This april it was sunny and warm more often than rainy and cold (got a sunburn within a few days!), but from what I heard it can vary from snow to 30 degrees Celsius, so you should be prepared for both. In the mountains it is colder, the nights especially, bring gloves, hat, scarf and a warm sleeping bag for colder days and the not so well heated albergues.
Spring is beautiful to watch, it seems to get greener from day to day, first flowers ect. - So if you don't mind not knowing what weather you'll get, spring is a good time to walk, in my opinion.
Route conditions:
When it's raining there's a lot of mud, in Galicia there were some puddles so large it was a bit tricky getting around them, but that's better than asphalt, isn't it? Overall the route was in good condition and easy to walk, but I guess that varies from year to year and snow and rain can change that quickly in some areas (mountains especially). Heard of people who had to take a bus around Cebreiro one year because of snow, but only hearsay, so maybe others can tell you more about that.
Albergues:
In april most are open, only some of the summer-only albergues were closed. Some are well heated, some not. Bars were open also, you can have a coffee or stop to sleep every few kilometers in some parts of the route
I wish you Happy Camino Planning!