It will add to your assets for Swiss wealth tax purposes - net of any mortgage.
The Swiss hypothetical rental will not apply to a foreign property.
You cannot deduct foreign mortgage interest payments from Swiss taxes.
Real estate income is only taxed in the country where it's located - if any.
In Kanton Zürich you can.
Several tax advisers I've had over the years disagree with you.
But.. this year I might phone up and ask if I have to include in my 2021 return
Again this income will influence your taxation rate hence your taxes even though you indeed do not pay income tax in CH - but it’s not tax neutral in CH as you need to declare worldwide income to determine your tax rate.
It depends on the tax agreements between the two countries but certainly for the UK it's true from the Swiss perspective.
For Swiss tax return you're supposed to include *every* source of income and *every* taxable asset of which a property is one.
The term "not taxable in Switzerland" is not the same as "not declarable in Switzerland".
There are tax advisers who advise to break the rules, e.g. don't declare properties, company shareholdings, savings accounts etc. but of course this doesn't make them right. I know people who follow this advice and nothing bad has happened to them so far.