Rain gear for the Alps?

That is what I mean by heavy duty hiking, and I was just about OK wearing something like these Scarpa boots, but only because the weather conditions were perfect: https://bestwalkingboots.org/scarpa-ranger-2-gtx-activ-review/

In a steady/sustained rain, if you want to be outside for hours, you're correct in your belief that staying dry is important and an umbrella and "rain-proof" jacket won't work for the lower half of your body or your feet.

We were in Switzerland two years ago, and found the rain did not last all day, at least not the heavy rain. We hiked in the light showers.

Golf-type rain pants are great, and also add a little warmth, and aren't bulky to pack.

I have found shoes/ boots that are designed to be waterproof just aren't as comfortable as I'd like. I take my regular traveling shoes/boots and use waterproof spray [ 2-3 coats.] This has worked well for me.

I'd also suggest a raincoat that is knee- length; there are many packable styles. Some folks like rain ponchos, altho I find them too easily blown by wind.

Safe travels!

Yes, waterproof rain pants are a necessity for all day walks in the rain. Rain pants are essential on days with heavy wind driven rain. My rain pants are have breathable waterproof/windproof membranes (i.e. Gore-tex). I prefer side zip pants that can be put on without taking of my boots but the zippers are a point of vulnerability even with Velcro storm flaps.

On days with heavy all day rain, carry extra dry socks. my boots are Gore-tex lined but water drips down my legs soaking my socks.

I cannot predict how much rain you might encounter. But in preference to packing something you may never use, consider quick-drying pants that have multiple uses. Also, the easier trails around Muerren are generally not far from some type of village, shelter, bar, or alternate transport (check maps).

If the weather is warm then wearing quick-dry pants as Laura suggests is a great idea. But if it's cool and breezy you may get cold before you get dry. There are light weight packable rain pants at REI. I'm sure those from Beans would be fine. And if Beans says the shoes you are considering are waterproof then I'm sure they are too. Try them out and walk around the house for a day or two. Bean's return policy is pretty generous.

We did not use rain pants when we did the Alpine My Way tour in September several years ago. We had rain but mostly on bus days. But we did use rain pants (probably from REI) when hiking in Scotland, and were very grateful for it. Even if it didn't rain, they provided a nice layer against the cold when necessary. On other trips, when my husband has cycled some, we put his cycling clothes in one of those vacuum bags. They did not take up much room, and were easy to keep separate when not needed.

There are a few great little stores right in Murren with all kinds of weather proof clothing and accessories. I've only been to Murren once where it rained every single day all day long - and I've been more times than I can count.

https://www.regatta.com/pack-it-waterproof-overtrousers-black/
I have a pair of these very light waterproof trousers, very light (about 200g) Ideal for summer walking and you can wear them all day as they are breathable.i just pack them in my bag wherever i go and they have helped me out several times.

As long as your core is warm and your feet aren’t submerged a good water proof shoe should fit the bill. Longer hikes above the tree line I would say more. Though you don't seem to hike far from shelter hypothermia is always a possibility in higher elevations and cooler temps. Be prepared at higher elevations. A small ruck with rain jackets/suits and umbrellas is a lite pack.

Some good thoughts above. The decision to buy/bring rain/wind pants or not depends on potential threat and consequences of failure.

As Laura notes, rain pants may not be needed if you are close to shelter. Rain paints would definitely be overkill for walking around areas with shops and cafes. Risk of getting wet and cold may or may not be high, but the consequence are low when walkers can pop into a warm cafe.

On the other hand, if you are on all day walks away from shelter, hypothermia can be a risk with air temperatures in the mid-40s F, wind and rain. High risk and high consequences (potential death from exposure).

https://www.yr.no/place/Switzerland/Bern/M%C3%83%C2%BCrren/statistics.html
June 11.2°C normal 16.2°C high 6.7°C low 15 days precipitation

I always pack a rain proof shell. My preferences are adjustable hood, long enough so water drips past your butt, zippers and zippered pockets that have rain proof flaps and something breathable/comfortable to wear. I bring one or two warm layers (sweater, down jacket, etc.) that can be worn under the shell, depending on temperature.

I don't pack rain pants but I do travel with golf pants. I've found golf pants are light weight, low bulk, quick dry, non-wrinkle, comfortable to hike in while looking nice enough to wear to dinner. I leave the heavy, bulky, slow-drying, hard to launder jeans at home when I travel.

I did bring some rainproof Rockport's to Ireland last trip but usually something that can take some rain is fine. As far as "hiking" shoes are concerned. I wouldn't pack a dedicated hiking boot unless that was the primary purpose of the trip. Virtually every trail I've walked on could probably be done in flip flops. I like some traction on the bottom but try to stay with something suitable for walking all day that can still be worn to a restaurant for dinner.

I also pack non-cotton socks. Cotton loses both padding and insulation value when it gets wet (applies to shirts, pants, sweaters too), making them worthless for a pack list. Pack either synthetic or wool socks. Mine are normally non-cotton crew or ankle socks made by a sports brand out of a synthetic (If it's going to be cold, I pack wool hiking socks).

I don't pack an umbrella. If it's windy, it's more hassle than help. If an umbrella will help, everywhere sells a 5 euro version (that won't survive any wind).

Can I suggest that, instead of investing in pants you'd have to change in and out of, and pack around, you try using a Nikwax product and make a couple pair of your current pants waterproof or (at a minimum) water resistant? I use it every year in the Seattle/Washington State & Alaska environments when I spend 14-16 hours a day outside in all kinds of weather.

And yes, I know what the weather's like in Germany and Switzerland; I spent almost 4 years over there. Good boots, a decent jacket, and a good hat are your main defense.