I started out years ago relying on primarily a poncho for rain protection, and a bucket hat for sun protection. Over the years, I experimented with nearly everything that came along.
One lesson learned is that, when walking in the bright hot sun of Spain, a UV resistant umbrella DOES reduce the temperature underneath by about 20 degrees Fahrenheit, much in the same fashion that being in the shade of a tree will do.
While standing in the sun on the street in Santiago, when working as a volunteer in the summer, I would frequently use my Euroschirm umbrella. It works.
On the other hand, the problem with "hands-free" umbrellas is the effort you need to go through to make it ride correctly when you are using it with hiking poles. Mine seems to bounce all over the place. Also, when road-walking, I would frequently have to readjust the umbrella whenever a truck or bus passed me. It liked to flip inside-out.
To make my point, in 2018, starting the Camino de Invierno one morning, I was walking with a fellow from the Netherlands. It started to drizzle, and I began the 5 minute process of mounting my Euroschirm umbrella on my rucksack harness.
As I was playing with this, my Dutch friend reached back and pulled a red Totes umbrella from his rucksack side-pocket. It took him one moment to snap it open, and a second to wedge it in his sternum strap, with the shaft resting on his shoulder. Voila, in maybe 10 seconds he was protected from the rain.
Clearly, this is not a solution for heavy rain or a windy, driving rain. But, then, no one uses an umbrella anyway.
More years of research led me to a solution for still weather sun and rain - a lightweight UV resistant GOLF umbrella in neon Yellow (safety for road walking). When not used, it rides in a side rucksack mesh pocket. When deployed, it gets shoved in my sternum strap. The long shaft has a hand loop, that is secured with a nylon cord that I wrap around my rucksack waist belt. This applies a downward force to keep the shaft more or less vertical and resting on my shoulder. Simple but effective. The long umbrella shaft appears to be the critical factor.
The key is to find an umbrella that works for YOU. Choose the appropriate diameter, dome height, number of ribs (wind resistance), UV resistance, and color. In the end I found my best solution in Decathlon. But remember, this is a GOLF umbrella, not a trekking umbrella. SO, I went to the GOLF department.
My personal solution for heavy rain or rain and wind continues to be a Sea to Summit Sil-Nylon poncho. I long-ago Super-Glued the snaps so they would not easily come apart in the wind. I just suck up the fact that I am going to sweat like a pig in the poncho.
To keep vision good, I find that a baseball type cap is best. It keeps the water off my eyeglasses and does not allow rain to run down my back. If you wear a bucket-style cap under a poncho hood, the rim acts as a 'gutter' to channel water around the back and down your neck.
If walking on a dry day, with bright hot sun, then a Tilley or bucket style cap remains the best, at least IMHO. Don't forget a Buff. On a brutally hot sunny day - like on the Meseta - wet it, then wear it on your head, or around your neck to aid in cooling through evaporation.
Bottom line, when on Camino, I carry a baseball cap, bucket cap, S2S very lightweight poncho and a Decathlon GOLF umbrella. It works for me.
Hope this helps.
Tom