self-service laundry in London or Zurich

Mentioning this service as a back-up. They do a great job.

https://www.laundryheap.com/en-gb/london

There are self service laundromats all over London. In and out in just over an hour.

Last spring I stayed at The Bailey's across from Gloucester Road Station and used the laundromat near Earl's Court Station.

look for the term launderette in London

There are many self service launderettes in London. Two that I have used since the pandemic are:
1) Radiant Dry Cleaners and Launderette on Hogarth Road. This is close to the Earls Court tube station. There is usually an attendant in the dry cleaning area who will make change for you (it takes pound coins). I have used this several times while staying at a hotel (that is now closed) near Earls Court. You could also buy a laundry detergent pod from the attendant.
2) Kings Launderette on Cromer St. This is a short walk from the St Pancras Premier Inn and I used it when I stayed there. There was an attendant who could make change.

Some of the aparthotels (e.g., Wilde, Locke, Staybridge Suites) have washers either in the room or in a laundry room available for guests. On booking.com, you can filter on “washing machine” under room amenities.

In Europe, I'm finding several aparhotels that list washing machine as an amenity. I know that there are machines that both wash and dry clothes in the same machine, but is that a safe assumption given that it says washing machine?

The following hotel chains have self service laundry rooms. (Some free, some charge.) They have separate washers and dryers:

Staybridge Suites
Hyatt House
Residence Inns
Locke Hotels
Wilde by Staycity
Staycity
Native Hotels
Citadines
Fraser Suites

In Europe, I'm finding several aparhotels that list washing machine as an amenity. I know that there are machines that both wash and dry clothes in the same machine, but is that a safe assumption given that it says washing machine?

No. You can’t assume that there will be a dryer or that the washing machine is a combo model that also dries. The aparthotel website should provide more detail. If it says laundry room or washer/dryer, there is a machine that dries clothes. If it only says washing machine, then it could be just a washer. I’ve stayed in some apartments with a washing machine and a drying rack so you can hang your clothes to dry.

Some places also refer to a drying rack as a "dryer". And the combo washer/dryer is not known for its capacity or drying capabilities. You could spend all day washing small loads in the combos or visit a nearby laundromat/launderette and be done quickly.

The in-apartment washing machines and dryers I’ve encountered in Europe have been disappointing and time-consuming at best. On a recent 6 week trip, at one stop we had an apartment with a washer/dryer and at 2 other stops we used local self-service launderettes, in addition to sink washing. I’ll take a launderette any day. At the Leipzig Adina, an otherwise lovely hotel, the small combo washer/dryer machine took 2 hours per wash cycle and another 2 hours for the dry cycle with frequent isn’t-it-dry-yet !?! checks. That was for one load. Not a relaxing or efficient use of our evening At the laundromats we found in Vienna and Karlsruhe, we averaged about 90 minutes to do two loads of laundry. And, we had opportunities for some nice conversations with locals.

When booking a hotel for a stay that includes a laundry day, I search Google Maps to verify there is a nearby self-serve launderette. I sometimes find one very close to my hotel (Paris especially) but don’t make that a top priority when booking. If I’m within a 15 or 20 minute walk or bus ride — that’s close enough. Like your wife, I’m very particular about my laundry so I bring my own High-Efficiency soap powder and Shout Color Catchers.

I can’t comment for the whole of Europe but in the UK if it is just mentioning a ‘washing machine’ it is unlikely to be one that drys as well. One that does both is often referred to as a ‘washer dryer’.
Stand-alone dryers are sometimes referred to as ‘tumble dryers’ although that is a bit old school. Drying racks are more commonly called ‘clothes airers’ or just airers.
All modern machines have cycles of different lengths so there shouldn’t be the need to be limited to slow washing cycles. If the manual for a machine isn’t available it can be easily found on the internet where the machine hieroglyphics will be explained.
Speaking as someone who has never owned a dryer, doing on extra spin at the end of a wash can really help with drying for clothes that tend to hold water. Also properly spacing clothes out on the airer so they don’t overlap and having the airer in an area with a flow of air.

I don't know how likely you are to find this in a rental but having a dehumidifier on does also really speed up the drying process.