Hi and welcome to the forum!
The "best time for walking" depends a lot on personal preference, which section you plan to walk, and what you consider crowded.
Personally, I prefer a summer start for the Francés, because from St. Jean on it is more quiet than for example in may or september, and there's no need to make reservations for beds. It only gets very busy in Galicia, but there are strategies how to still have an enjoyable walk there during high season. I love the spanish dry heat and the meseta in the baking sun, and the early morning starts, so for me a june/july/august Francés is a personal favourite.
Others prefer winter or very early spring / late fall.
With regard to crowds, the worst times to walk are the Francés from St. Jean in april/may and september, and the part in Galicia in july/august.
So, keep in mind, those sections have different high seasons.
Sarria-Santiago really is a giant conga line in july/august, but only if you stop at the popular "end of stage" towns and start walking early with the crowds. If you stay in smaller places inbetween and walk in the afternoon, it can still be a more quiet walk.
So it depends.
Have fun planning, and buen Camino